PRIMARY OBJECTIVES:

I. To estimate the maximum tolerated dose (MTD) or recommend a Phase II dose of AZD6244 (selumetinib) in children with recurrent or refractory low-grade glioma. (Phase I, completed as of April 29, 2013) II. To describe the toxicity profile and define the dose limiting toxicity of AZD6244 in children with recurrent or refractory low-grade glioma. (Phase I) III. To study the safety of the maximum tolerated dose (MTD) or recommended a Phase II dose (RP2D) of AZD6244 as determined based on safety data from children \>= 12 years of age in children \< 12 years of age; if the MTD/RP2D of the older children is too toxic for the younger children, we will de-escalate to one dose level below and study the safety of that dose in the younger age cohort. (Phase I) IV. To assess the sustained response rate of AZD6244 administered at 25 mg/m\^2/dose twice daily (BID), in a single arm Phase II setting in patients assigned to strata based on neurofibromatosis (NF)-1 status and presence or absence of v-raf murine sarcoma viral oncogene homolog B (BRAF) aberrations, specifically BRAF V600E mutations and/or BRAF KIAA1549 fusion identified by immunohistochemistry (IHC) and fluorescence in situ hybridization (FISH), respectively. (Phase II, completed as of January 4, 2021) V. To estimate the sustained response rate and prolonged disease stabilization rate (defined as lack of disease progression for \>= 12 courses) associated with AZD6244 in patients with recurrent and/or progressive low-grade gliomas who previously received treatment on PBTC-029 or PBTC-029B for a minimum of 12 courses, with at least stable disease or patients who had a sustained response but remained on treatment \< 12 courses. (Re-treatment Study, enrollment complete as of April 23, 2019)

SECONDARY OBJECTIVES:

I. To characterize the inter- and intra-patient variability in AZD6244 pharmacokinetics administered on this schedule and to assess the influence of patient specific covariates (including concomitant drug therapy) on AZD6244 pharmacokinetics. (Phase I) II. To evaluate the feasibility of collecting pre-trial tumor samples and the feasibility of using in situ hybridization assay to identify BRAF aberrations in available tumor specimens. (Phase I) III. To determine if pre-trial tumor samples show the biochemical signature that indicates activation of the mitogen-activated protein kinase (MAPK) pathway. (Phase I) IV. To describe magnetic resonance imaging (MRI) characteristics of the tumors before and after treatment and to explore the diffusion changes in the tumors before and after treatment to determine if there is an early diffusion indicator of response. (Phase I) V. Within the constraints of a Phase I trial, to document antitumor activity of treatment with AZD6244, as measured by objective responses and progression-free survival (PFS). (Phase I) VI. To explore the pharmacogenetic polymorphisms in AZD6244 metabolizing enzymes and transporters and relate these polymorphisms to AZD6244 pharmacokinetics. (Phase I) VII. To estimate the PFS distributions associated with AZD6244 treatment separately in patients assigned to the six strata as well as for various other subsets e.g. histology and tumor grade across strata. (Phase II) VIII. To explore correlations between BRAF aberrations and treatment response and PFS in patients for whom relevant biology data are available. (Phase II) IX. To assess MAPK aberrations by a combination of whole-exome and ribonucleic acid (RNA) sequencing. (Phase II) X. To characterize the inter- and intra-patient variability in AZD6244 pharmacokinetics administered on this schedule at the MTD/RP2D. (Phase II) XI. To determine progression-free survival following re-treatment with AZD6244 for progressive, recurrent low-grade gliomas and to evaluate the impact of variables such as previous response, interval treatment regimens, BRAF status and previous dose of AZD6244. (Re-treatment Study) XII. To evaluate the toxicity profile of re-treatment with AZD6244 and correlate with toxicities seen during initial treatment. (Re-treatment Study) XIII. To evaluate the toxicity profile of re-treatment with AZD6244 beyond 2 years for those patients who continue to show benefit from the drug, i.e. at least stable disease (SD). (Re-treatment Study)

OUTLINE: This is a phase I dose-escalation study (completed as of April 29, 2013) followed by a phase II study.

Patients receive selumetinib orally (PO) twice daily (BID) on days 1-28. Cycles repeat every 28 days for up to 26 cycles in the absence of disease progression or unacceptable toxicity. Patients who experience a sustained objective response from selumetinib on the phase I or phase II portions of the trial, and who have completed 2 years of treatment and stopped study drug may be enrolled on the re-treatment study after progression/recurrence. Patients in the re-treatment study may continue treatment indefinitely in the absence of disease progression or unacceptable toxicities. Patient undergo blood sample collection on study.

After completion of study treatment, patients are followed up for 30 days.