Inclusion Criteria:  1. Written informed consent of the patient's LAR, and assent when appropriate based on the patient's age and institutional guidelines, prior to any study-related procedure.  2. Patients must have progressive, refractory, or recurrent HGG (WHO Grade III or IV).  3. Age ≥2 to <18 years at the time of the first Berubicin dose. 4. Performance status score ≥50 (Lansky for research patients aged ≤16 years and Karnofsky for patients ˃16 years). Patients 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.  5. Patients must have completed at least 1 line of prior therapy. 6. Before the projected start of scheduled study treatment, the following time periods must have elapsed:  5 half-lives from any investigational agent. 4 weeks from cytotoxic therapy (except 23 days from temozolomide and 6 weeks from nitrosoureas). 6 weeks from antibody therapies. 4 weeks (or 5 half-lives, whichever is shorter) from other antitumor therapies.  Patients who have received radiation therapy must be ≥6 weeks post the completion of local palliative radiation therapy (re-irradiation for progressive disease or upfront radiation therapy at initial diagnosis).  7. Adequate organ function defined as:  a. Bone marrow: i. Peripheral absolute neutrophil count ≥1000/mm3 ii. Hemoglobin ≥8 g/dL (may have received packed red blood cell transfusion) iii. Platelet count ≥100,000/mm3 (transfusion-independent, defined as not receiving platelet transfusions for at least 7 days prior to enrollment) b. Renal function: i. Creatinine clearance or radioisotope glomerular filtration rate ≥70 mL/min/1.73 m2 or normal serum creatinine based on age c. Hepatic function: i. Total bilirubin (sum of conjugated + unconjugated) ≤1.5 × the upper limit of normal (ULN) for the institution ii. Alanine aminotransferase ≤3 × ULN for the institution iii. Serum albumin ≥2 g/dL d. Neurologic function: i. Patients with seizure disorder may be enrolled if the seizure disorder is well controlled, as determined by the investigator.  e. Cardiac function (left ventricular ejection fraction [LVEF]): i. Fractional shortening ≥27% or LVEF ≥50% by echocardiogram or multigated radionuclide study (MUGA) 8. All adverse events (AEs) Grade >1 related to prior therapies (chemotherapy, radiation therapy, and/or surgery) must be resolved to Grade 1 or baseline level, except for alopecia and sensory neuropathy Grade ≤2 or other Grade ≤2 AEs not constituting a safety risk based on the investigator's judgment.  9. For postpubertal patients: Female patients must agree to use highly effective contraception during the period of the study and for at least 90 days after completion of treatment. Male patients must be surgically sterile or must agree to use highly effective contraception during the period of the study and for at least 3,5 months (no less than 104 days) after completion of treatment. Details are provided in the full protocol.  10. Female patients of childbearing potential aged 10 years or older must have a negative serum or urine pregnancy test.  11. MRI of the brain and entire spine (including all sites of disease), within 10 days prior to start of study drug.  12. Corticosteroid dose must be stable or decreasing for at least 5 days prior to the baseline MRI scan.  Exclusion Criteria:  1. Evidence of diffuse leptomeningeal disease or evidence of cerebrospinal fluid (CSF) dissemination.  2. Known additional malignancy that is progressing or has required active treatment within 3 years of start of study drug.  3. History of allergic reactions attributed to compounds of similar chemical or biologic composition to Berubicin or its excipients.  4. Patients with any clinically significant, unrelated systemic illness (eg, significant pulmonary, hepatic [including Gilbert's syndrome], or other organ dysfunction) or psychiatric illness/social situations that would compromise the patient's ability to tolerate the study drug or study procedures or would likely interfere with the study procedures or results.  5. Any known clinically significant active bacterial, fungal, or viral infection including hepatitis B or hepatitis C, or any underlying disease in the recent past that could compromise enrollment and the safety of the patient.  6. Patient with a history of clinically significant, uncontrolled heart disease and/or repolarization abnormalities as documented by a standard 12 lead electrocardiogram (ECG).  7. Known history of cardiac arrhythmias including atrial fibrillation, tachyarrhythmias, or bradycardia, unless arrhythmia is controlled and after a cardiology consultation has cleared the patient to receive Berubicin. Patients receiving therapeutic agents known to prolong QT interval will be excluded; however, the use of ondansetron is permitted. Patients with a history of congestive heart failure, myocardial infarction, or stroke in the last 3 months will be excluded.  8. Congenital long QT syndrome or QTc >460 ms. 9. Patients receiving any other anticancer or investigational drug therapy. 10. Prior treatment with bevacizumab. 11. Current or planned participation in a study of another investigational agent or using an investigational device.  12. Requirement for cytochrome P450 3A4 (CYP3A4)-inducing or inhibiting agents, with the exception of corticosteroids.