A Study of Pomalidomide Monotherapy for Children and Young Adults With Recurrent or Progressive Primary Brain Tumors

The study will consist of 4 parallel groups of participants, one for each of the following primary brain tumor types: high-grade glioma, medulloblastoma, ependymoma and DIPG. A Simon's Optimal two-stage study design will be applied to each group and enrollment will occur as follows: * Stage 1: Nine participants will be enrolled in each brain tumor type group * Stage 2: If during Stage 1, ≥ 2 participants achieves either an objective response (either complete response or partial response) within the first 6 cycles of treatment (or within the first 3 cycles for DIPG participants), or a long-term stable disease, an additional 11 participants shall be enrolled; otherwise no additional participants will be enrolled into that group. * If a total of 5 or more participants across all 20 participants in a given group (Stage 1 and 2) evaluable for the primary endpoint are observed as having either an objective response (either complete response or partial response) within the first 6 cycles of treatment (or within the first 3 cycles for DIPG participants) or a long-term stable disease, pomalidomide will be considered effective in that disease indication. Once treatment has been discontinued, participants will be followed up for up to 5 years from enrollment of the last participant. Participants who withdraw from either stage for reasons other than disease progression prior to completing Cycle 1 of study treatment will be replaced.