Inclusion Criteria: Screening Phase  Participants with histologically confirmed or suspected low-grade glioma, including neuronal and mixed neuronal-glial tumors Participant must have adequate tumor tissue from primary and/or relapsed tumor for central pathology review Projected to be ≥ 2 years and < 25 years at the time of study enrollment  Participant's body surface area (BSA) at time of study enrollment must fall within the range outlined in the protocol for the specific dose level under evaluation:  Phase 1: Dose Finding/Dose-escalation  For Phase 1 participant's BSA must fall within the range specified in the protocol for the specific dose level under evaluation.  Phase 2: All Cohorts:  For Phase 2 of the study the upper BSA restrictions will be removed. Participant and/or guardian can understand and is willing to sign a written informed consent document according to institutional guidelines  Exclusion Criteria: Screening Phase  Participants with retinal pathology on ophthalmologic examination that is consistent with or a precursor for central serous retinopathy, retinal vein occlusion (RVO), or neovascular macular degeneration Participants with a known malabsorption syndrome or preexisting gastrointestinal conditions that may impair absorption of mirdametinib (e.g., gastric bypass, lap band, or other gastric procedures) Participant with a known history of liver disease or known hepatic or biliary abnormalities (except for Gilbert's syndrome or asymptomatic gallstones) Participants with a clinically significant history of chronic interstitial lung disease (such as bronchopulmonary dysplasia, chronic bronchiolitis, obliterative bronchiolitis, chronic aspiration pneumonia, surfactant protein disorder, or other serious chronic pulmonary condition). Participants with a history of asthma, reactive airways disease, or viral pneumonitis are not to be excluded if disease has resolved or is well-controlled.  Inclusion Criteria: Phase 1 and Phase 2, All Cohorts  Participant must be ≥ 2 years and < 25 years of age at the time of enrollment  Participant's BSA at time of study enrollment must fall within the range outlined below for the specific dose level under evaluation:  Phase 1: Dose-finding/Dose-escalation  For Phase 1 participant's BSA must fall within the range specified in the protocol for the specific dose level under evaluation.  Phase 2: All Cohorts  For Phase 2 of the study the upper BSA restrictions will be removed.  Participant must have confirmation of one of the following diagnosis per St. Jude Children's Research Hospital central pathology review of primary and/or relapsed tumor:  Eligible tumors include:  Low-grade glioma/astrocytic tumor/glioneuronal tumor/neuroepithelial tumor, not otherwise specified (NOS) or not elsewhere classified (NEC) Pilocytic astrocytoma Pilomyxoid astrocytoma Pleomorphic xanthroastrocytoma Ganglioglioma Gangliocytoma Diffuse glioma, diffuse astrocytoma, oligodendroglioma, or oligoastrocytoma Papillary glioneuronal tumor Rosette-forming glioneuronal tumor Diffuse leptomeningeal glioneuronal tumor Central neurocytoma, extraventricular neurocytoma Angiocentric glioma Dysembryoplastic neuroepithelial tumor (DNET), septal DNET, myxoid glioneuronal tumor Tectal glioma Desmoplastic infantile astrocytoma / ganglioglioma Polymorphous low-grade neuroepithelial tumor of the young Multinodular and vacuolating neuronal tumor In addition, tumor on central review must show evidence supporting MAPK pathway activation as defined by IHC, FISH and/or DNA/RNA sequencing (i.e. BRAF fused or rearranged, FGFR1/2/3 aberration, PTPN11, SOS1, RAF1 mutations, MYB or MYBL1 fused or rearranged, etc.) or occur in a participant with known NF1, NF2, SOS1, RAF1, or PTPN11 germline mutation. (Note: tests that show evidence supporting MAPK pathway activation that have been already performed do not need to be repeated as long as deemed acceptable by central review).  Participant must have measurable or evaluable disease (as defined in the protocol)  Note: Participants with metastatic disease or multiple independent primary LGGs are allowed on study. Participants who are receiving corticosteroids must be on a stable or decreasing dose for at least 1 week prior to enrollment with no plans for escalation.  Participant must have a Lansky (<16 years) or Karnofsky (≥16 years) performance score of ≥ 50 and, in the opinion of the investigator, a minimum life expectancy of at least 6 weeks.  Note: Participants who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score.  Participant must have adequate bone marrow and organ function as defined as:  ANC ≥ 1.0 x 10^9/L without growth factor support within 7 days Platelet count ≥ 75x 10^9/L without support of a platelet transfusion within 7 days Hemoglobin ≥8.0 g/dL without support of a blood transfusion within 7 days Potassium, total calcium (corrected for serum albumin), magnesium, sodium and phosphorus must be ≤ grade 1 or corrected to ≤ grade 1 with supplements before first dose of study medication Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x ULN. For the purposes of this study the ULN of ALT and AST is 45 U/L. Total bilirubin ≤ ULN; or if > ULN then direct bilirubin ≤ 1.5 x ULN  Adequate renal function defined as:  Serum creatinine ≤ the maximum serum creatinine based on age/gender: Age: 2 to < 6 years: maximum serum creatinine (mg/dL) 0.8 (male, female), Age: 6 to <10 years: maximum serum creatinine (mg/dL) 1 (male, female), Age: 10 to <13 years: maximum serum creatinine (mg/dL) 1.2 (male, female), Age: 13 to <16 years: maximum serum creatinine (mg/dL) 1.5 (male); 1.4 (female), Age: ≥ 16 years: maximum serum creatinine (mg/dL) 1.7 (male); 1.4 (female)  Adequate cardiac function defined as:  LVEF > 50% by ECHO QTc interval ≤ 450 msec for male participants, ≤ 470 msec for female participants after electrolytes have been corrected.  Hypertension:  Patients 2-12.99 years of age must have a blood pressure that is ≤ 95th percentile +10 mmHg for age, height, and gender at the time of enrollment (with or without the use of anti-hypertensive medications).  Patients ≥ 13 years of age must have a blood pressure ≤ 140/90 mmHg at the time of enrollment (with or without the use of anti-hypertensive medications).  Note for patients of all ages: Adequate blood pressure can be achieved using medication for the treatment of hypertension. Participants of childbearing/child-fathering potential must agree to use contraception. Participants and/or guardian have the ability to understand and the willingness to sign a written informed consent document according to institutional guidelines. Participants who are receiving P-gp and BCRP inhibitors must have received their last dose a week or 5 half-lives (whichever is greater) prior to the first mirdametinib dose.  Inclusion Criteria: Phase 1: Progressive or Recurrent Low-Grade Glioma without Previous MEKi exposure  Participant's tumor must have unambiguously progressed, relapsed, or recurred during or after the most recent prior therapy (chemotherapy or radiotherapy) and pseudoprogression or treatment-related tumor changes have, in the opinion of the investigator, been thoroughly vetted.  Progression may be radiographic or clinical (i.e. vision deterioration thought to be related to tumor in patients with optic pathway tumors, or neurologic deterioration thought to be related to tumor) but it must be unequivocal and sufficient to warrant treatment in the opinion of the investigator.  Prior therapy:  Patients who have received the following:  ≤ 3 prior treatment regimens with either myelosuppressive chemotherapy or biologic agents and/or focal radiotherapy Note that a treatment regimen is defined as a single agent (chemotherapeutic or biologic), or a sequential combination of therapies that can include radiotherapy (with or without concurrent radiosensitizer, chemotherapy, or biologic therapy) followed by maintenance therapy (either single or combination) given over a period of time at either diagnosis or relapse.  Chemotherapy:  Participant must have received their last dose of myelosuppressive anticancer chemotherapy at least 21 days prior to study enrollment or at least 42 days if nitrosourea.  Monoclonal antibody treatment and agents with known prolonged half-lives:  Patient must have recovered from any acute toxicity potentially related to the agent and received their last dose of the agent ≥ 28 days prior to study enrollment  MEK inhibitors:  Patients must not have received prior exposure to any MEK inhibitors  XRT/External Beam Irradiation including Protons:  Participant must have had their last fraction of radiation ≥ 3 months prior to study enrollment  Inclusion Criteria: Phase 2, Cohort 1: Newly Diagnosed and/or previously untreated (except surgery) Low-Grade Glioma  No prior anti-cancer treatment except surgery. In the opinion of the investigator tumor must warrant treatment defined as any of the following: unsafe to observe, unequivocally progressing on serial imaging, tumor is causing or at high risk of causing neurologic or vision-related deficits.  Inclusion Criteria: Phase 2, Cohort 2: Progressive or Recurrent Low-Grade Glioma without Previous MEK Inhibitor Exposure  Participant's tumor must have unambiguously progressed, relapsed, or recurred during or after the most recent prior therapy (chemotherapy or radiotherapy) and pseudoprogression or treatment-related tumor changes have, in the opinion of the investigator, been thoroughly vetted.  Progression may be radiographic or clinical (i.e. vision deterioration thought to be related to tumor in patients with optic pathway tumors, or neurologic deterioration thought to be related to tumor) but it must be unequivocal and sufficient to warrant treatment in the opinion of the investigator.  Prior therapy:  Chemotherapy:  Participant must have received their last dose of myelosuppressive anticancer chemotherapy at least 21 days prior to study enrollment or at least 42 days if nitrosourea.  Monoclonal antibody treatment and agents with known prolonged half-lives:  Patient must have recovered from any acute toxicity potentially related to the agent and received their last dose of the agent ≥ 28 days prior to study enrollment  MEK inhibitors:  Patients must not have received prior exposure to any MEK inhibitors  XRT/External Beam Irradiation including Protons:  Participant must have had their last fraction of radiation ≥ 3 months prior to study enrollment. Note that for this cohort, there are no limitations on number of prior treatment regimens and participants who have received craniospinal radiation are eligible  Inclusion Criteria: Phase 2, Cohort 3: Progressive or Recurrent Low-Grade Glioma with Previous MEK inhibitor Exposure  Cohort 3A (MEKi responders): Patients who previously received 6 or more cycles of any MEK inhibitor (including mirdametinib) and did NOT progress while on active MEK inhibitor therapy.  The progression must have occurred off MEK inhibitor therapy Participant's tumor must have unambiguously relapsed or clinically progressed. Progression may be radiographic or clinical (i.e. vision deterioration thought to be related to tumor in patients with optic pathway tumors, or neurologic deterioration thought to be related to tumor) but it must be unequivocal and sufficient to warrant treatment in the opinion of the investigator. Patient must not have discontinued MEKi (specifically mirdametinib) for unacceptable toxicity, and in the opinion of the PI be able to tolerate subsequent courses of MEKi therapy. Patients must have received treatment with a MEK inhibitor for ≥6 cycles and showed no signs of progression while on active MEK inhibitor therapy. Patients who received additional anti-tumor therapy following discontinuation of MEK inhibitor can be enrolled in this cohort.  Prior Therapy:  Chemotherapy:  Participant must have received their last dose of myelosuppressive anticancer chemotherapy at least 21 days prior to study enrollment or at least 42 days if nitrosourea.  Monoclonal antibody treatment and agents with known prolonged half-lives:  Patient must have recovered from any acute toxicity potentially related to the agent and received their last dose of the agent ≥ 28 days prior to study enrollment.  MEK inhibitors:  Participant must have received their last dose of MEKi at least 3 weeks prior to study enrollment.  XRT/External Beam Irradiation including Protons:  Participant must have had their last fraction of radiation ≥ 3 months prior to study enrollment. Note that for this cohort, there are no limitations on number of prior treatment regimens and participants who have received craniospinal radiation are eligible  Cohort 3B (MEKi non-responders): Patients with previous exposure to alternative MEK inhibitors (excluding mirdametinib) who progressed while on active MEK inhibitor therapy  Participant's tumor must have unambiguously relapsed or clinically progressed. Progression may be radiographic or clinical (i.e. vision deterioration thought to be related to tumor in patients with optic pathway tumors, or neurologic deterioration thought to be related to tumor) but it must be unequivocal and sufficient to warrant treatment in the opinion of the investigator. Progression or recurrence must have occurred while on active MEK inhibitor therapy (excluding mirdametinib) Participants are eligible regardless of how many prior cycles were received or prior history of response (i.e. PR, Major Response, or CR) Patients who received additional anti-tumor therapy following discontinuation of MEK inhibitor can be enrolled in this cohort as long as they meet the above criteria.  Prior Therapy:  Chemotherapy:  Participant must have received their last dose of myelosuppressive anticancer chemotherapy at least 21 days prior to study enrollment or at least 42 days if nitrosourea.  Monoclonal antibody treatment and agents with known prolonged half-lives:  Patient must have recovered from any acute toxicity potentially related to the agent and received their last dose of the agent ≥ 28 days prior to study enrollment.  Alternative MEK inhibitor:  Participant must have received their last dose of MEKi (excluding mirdametinib) at least 3 weeks prior to study enrollment.  XRT/External Beam Irradiation including Protons:  Participant must have had their last fraction of radiation ≥ 3 months prior to study enrollment. Note that for this cohort, there are no limitations on number of prior treatment regimens and participants who have received craniospinal radiation are eligible.  Exclusion Criteria: Phase 1 and Phase 2, All Cohorts  Participants whose tumor on central review is any of the following:  High-grade (WHO III or IV) Subependymal giant cell astrocytoma Ependymoma Histone H3 K27M/K28M or G34/G35-mutant BRAF V600 mutant NTRK1/2/3, ALK, or ROS1 fusion-positive IDH 1/2 mutant Participant who is currently receiving any other anticancer or investigational agents (^11C-methionine allowed) or still recovering from acute toxicity potentially related to the agent.  Ophthalmologic Conditions  Patients with central serous retinopathy Patients with retinal vein occlusion or retinal detachment  Patients with uncontrolled glaucoma  If checking pressure is clinically indicated and feasible per patient's age and ability to complete exam, patients with IOP > 22 mmHg or ULN adjusted by age are not eligible Participants with other clinically significant medical disorders (i.e. serious infections or significant cardiac, pulmonary, hepatic, psychiatric, or other organ dysfunction) that in the investigator's judgement could compromise their ability to tolerate or absorb protocol therapy or would interfere with the study procedures or results. Sexually active patients of reproductive potential who have not agreed to use an effective contraceptive method for the duration of their study participation and for 16 weeks after stopping study therapy are not eligible. Participants are excluded if unable to comply with protocol guidelines.