In recent years, the classification of adult-type diffuse gliomas has undergone a revolution, wherein specific molecular features now represent defining diagnostic criteria of IDH-wild-type glioblastomas, IDH-mutant astrocytomas, and IDH-mutant 1p/19q-codeleted oligodendrogliomas. With the introduction of the 2021 WHO CNS classification, additional molecular alterations are now integrated into the grading of these tumors, given equal weight to traditional histologic features. However, there remains a great deal of heterogeneity in patient outcome even within these established tumor subclassifications that is unexplained by currently codified molecular alterations, particularly in the IDH-mutant astrocytoma category. There is also significant intercellular genetic and epigenetic heterogeneity and plasticity with resulting phenotypic heterogeneity, making these tumors remarkably adaptable and robust, and presenting a significant barrier to the design of effective therapeutics. Herein, we review the mechanisms and consequences of genetic and epigenetic instability, including chromosomal instability (CIN), microsatellite instability (MSI)/mismatch repair (MMR) deficits, and epigenetic instability, in the underlying biology, tumorigenesis, and progression of IDH-mutant astrocytomas. We also discuss the contribution of recent high-resolution transcriptomics studies toward defining tumor heterogeneity with single-cell resolution. While intratumoral heterogeneity is a well-known feature of diffuse gliomas, the contribution of these various processes has only recently been considered as a potential driver of tumor aggressiveness. CIN has an independent, adverse effect on patient survival, similar to the effect of histologic grade and homozygous CDKN2A deletion, while MMR mutation is only associated with poor overall survival in univariate analysis but is highly correlated with higher histologic/molecular grade and other aggressive features. These forms of genomic instability, which may significantly affect the natural progression of these tumors, response to therapy, and ultimately clinical outcome for patients, are potentially measurable features which could aid in diagnosis, grading, prognosis, and development of personalized therapeutics.