Paediatric brain tumours have high rates of mutations in the histone variant H3.3 (H3.3 K27M, H3.3 G34R) and the H3.3-specific ATRX/DAXX chaperone complex. These H3.3 point mutations affect many chromatin modifications but exact oncogenic mechanisms are currently unclear. Histone H3.3 is known to localise to nuclear compartments known as PML nuclear bodies, which are frequently mutated in acute promyelocytic leukaemias. We find that H3.3 point mutations disrupt the formation of PML nuclear bodies and this prevents differentiation down glial lineages. Similar to PML-mutated leukaemias, H3.3-mutated patient-derived gliomas cells are also sensitive to drugs which target PML bodies. We also find that point mutations in IDH1/2 – which are common events in myeloid leukaemias and adult gliomas – also disrupt the formation of PML bodies. We identify PML as a contributor to oncogenesis in a subset of gliomas and show that PML-targeting strategies could be effective at treating these tumours.