Inclusion Criteria:

- MOLECULAR BIOLOGY STUDY

- Tumor: Subjects must have a histologically confirmed diagnosis of
medulloblastoma/PNET, ependymoma or HGG (such as anaplastic astrocytoma,
glioblastoma, gliosarcoma, or anaplastic oligodendroglioma) that is recurrent or
refractory to conventional therapy

- Subjects must have clinical indications for surgical resection and be amenable to
receiving imetelstat prior to tumor resection; subjects who require emergent surgery
are not eligible for the Molecular Biology study

- Subjects must provide, fresh flash frozen tumor samples (target 50 mg tissue; as low
as 20 mg is adequate) from the time of diagnosis or previous recurrence for the
assessment of tumor telomerase activity by the TRAP assay

- PHASE II STUDY

- Tumor: Subjects must have recurrent or refractory disease with a histological
diagnosis from either the initial presentation or at the time of recurrence; the
requirement for histologic verification is waived for subjects with DIPG (stratum D);
the following diagnoses are eligible and will be treated in separate strata (A-D): A)
Recurrent or refractory medulloblastoma/PNET; B) Recurrent or refractory high-grade
glioma, (such as anaplastic astrocytoma, glioblastoma multiforme, gliosarcoma,
anaplastic oligodendroglioma); C) Recurrent or refractory ependymoma; D) Recurrent or
refractory DIPG (diagnosis by imaging characteristics acceptable; no histologic
confirmation required)

- Slides from either initial diagnosis or relapse must be available for central
pathology review for Strata A-C; tissue slides must be sent; if tissue slides are
unavailable, the study chair must be notified prior to study enrollment

- All subjects must have bi-dimensionally measurable disease in the brain and/or spine,
defined as at least one lesion that can be accurately measured in at least two planes
in order to be eligible for this study.; subjects who are enrolled on the Molecular
Biology trial and who have measurable disease after the surgical resection and meet
all other eligibility criteria for the Phase II study will be counted towards the
accrual of the Phase II study

- FOR BOTH MOLECULAR BIOLOGY AND PHASE II STUDIES

- Subjects with neurological deficits should have deficits that are stable for a
minimum of one (1) week prior to registration; a baseline detailed neurological exam
should clearly document the neurological status of the subject at the time of
registration on the study

- Karnofsky >= 50% for > 16 years of age; Lansky >= 50% for children < 16 years of age
documented within 14 days of study registration and within 7 days of the start of
study drug administration

- Hemoglobin >= 8 g/dL (may receive blood transfusions)

- Absolute neutrophil count > 1,000/ul

- Platelet count >= 100,000/ul (transfusion independent defined as no platelet
transfusions with a 7-day period prior to enrollment)

- Serum bilirubin < 2.0 mg/dL (patients with Gilbert syndrome, serum bilirubin < 3.0 x
upper limit of normal [ULN])

- Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) =<
2.5 x institutional ULN

- Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5
x institutional ULN

- Alkaline phosphatase < 2.5 x institutional ULN

- Albumin >= 2 g/dL

- Adequate coagulation defined as activated partial thromboplastin time (aPTT) < 1.2 x
ULN

- Creatinine clearance or radioisotope glomerular filtration rate (GFR) >= 70
ml/min/1.73 m^2 or a serum creatinine based on age/gender as follows:

- Age 1 to < 2 years: maximum serum creatinine (mg/mL) 0.6 for males and 0.6 for
females

- Age 2 to < 6 years: maximum serum creatinine (mg/mL) 0.8 for males and 0.8 for
females

- Age 6 to < 10 years: maximum serum creatinine (mg/mL) 1 for males and 1 for
females

- Age 10 to < 13 years: maximum serum creatinine (mg/mL) 1.2 for males and 1.2 for
females

- Age 13 to < 16 years: maximum serum creatinine (mg/mL) 1.5 for males and 1.4 for
females

- Age >= 16 years: maximum serum creatinine (mg/mL) 1.7 for males and 1.4 for
females

- The threshold creatinine values were derived from the Schwartz formula for
estimating GFR (Schwartz et al. J. Peds, 106:522, 1985) utilizing child length
and stature data published by the Centers for Disease and Control (CDC)

- Subjects on systemic anticoagulants are excluded from this study as the drug can
cause minor, transient changes in aPTT

- Female subjects of childbearing potential must not be pregnant or breast-feeding;
female subjects of childbearing potential must have a negative serum or urine
pregnancy test; (pregnancy test must be repeated within 48 hours prior to the start
of therapy)

- Subjects of childbearing or child fathering potential must be willing to use a
medically acceptable form of birth control, which includes abstinence, while being
treated on this study

- Subjects must have recovered from the acute toxicities of all prior therapy before
entering this study; for those acute baseline adverse events attributable to prior
therapy, recovery is defined as a toxicity grade =< 2, using Common Terminology
Criteria for Adverse Events (CTCAE) v.4.0, unless otherwise specified in the
Inclusion and Exclusion Criteria

- Subjects must have received their last dose of known myelosuppressive anticancer
chemotherapy at least three (3) weeks prior to study registration or at least six (6)
weeks if nitrosourea

- Subjects must have received their last dose of investigational or biologic agent >= 7
days prior to study registration; in the event that a subject has received an
investigational or biologic agent and has experienced >= grade 2 myelosuppression,
then at least three (3) weeks must have elapsed prior to registration; if the
investigational or biologic agent has a prolonged half-life (>= 7 days) then at least
three (3) weeks must have elapsed prior to registration

- Subjects must have completed at least 3 half-life periods from the last dose of
monoclonal antibody prior to registration; Note: A list of half-lives of commonly
used monoclonal antibodies is available on the Pediatric Brain Tumor Consortium
(PBTC) website under Generic Forms and Templates

- Subjects must have received their last dose of radiation (XRT):

- 2 weeks prior to study registration for local palliative XRT (small volume)

- 3 months prior to study registration for craniospinal XRT

- 6 weeks (wks) prior to study registration for other substantial bone marrow
irradiation

- Subject must be >= 3 months since autologous bone marrow/stem cell transplantation
prior to registration

- Subjects who are receiving a corticosteroid, such as dexamethasone, must be on a
stable or decreasing dosage for at least 1 week prior to registration

- At least 7 days since the completion of therapy with a hematopoietic growth agent
(filgrastim, sargramostim, and erythropoietin) and 14 days for long-acting
formulations

- Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

- Subjects must not be receiving any other investigational agents

- Subjects with inability to return for follow-up visits or obtain follow-up studies
required to assess toxicity to therapy

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to imetelstat

- Known coagulopathy or bleeding diathesis

- Subjects with imaging evidence of CNS hemorrhage on baseline MRI obtained within 14
days prior to study enrollment are not eligible; Note: The presence of small punctate
areas consistent with hemorrhage will not exclude subjects from participation

- Use of systemic anticoagulant medications

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
serious infection, symptomatic congestive heart failure, unstable angina pectoris,
cardiac arrhythmia, cirrhosis or psychiatric illness/social situations that would
limit compliance with study requirements

- Pregnant women are excluded from this study because imetelstat is an investigational
agent with unknown potential for teratogenic or abortifacient effects; because there
is an unknown but potential risk for adverse events in nursing infants secondary to
treatment of the mother with imetelstat, breastfeeding should be discontinued if the
mother is treated with imetelstat; these potential risks may also apply to other
agents used in this study