Low-grade glioma (LGG) is a diffuse and infiltrative adult brain tumor. Due to the invasive nature of the tumor, surgical resection is rarely curative. LGG often undergo malignant progression and recur as a high-grade glioblastoma (GBM). The genomic and epigenomic landscapes of these tumors, particularly at recurrence, are understudied yet clinically important. Recurrent tumors may be driven by a distinct set of genetic and epigenetic alterations than their initial tumors, yet therapeutic decisions are often made based on profiling of initial malignancies. Here we comprehensively profiled 33 LGGs and their patient-matched recurrences, including cases with 2-6 intratumoral samples, with exome sequencing to identify somatic mutations, with the Infinium 450K array to investigate DNA methylation changes, and with RNA sequencing to measure gene expression changes. We found a wide range in the degree of evolution from initial to recurrence, in terms of both somatic mutations and DNA methylation changes. Tumors treated with the alkylating chemotherapy temozolomide (TMZ) often recurred with a hypermutation phenotype that was suggestive of therapy-driven malignant progression to GBM. Therapy-associated mutational activation of the AKT-mTOR pathway was a consistent feature of these hypermutated recurrences, which promoted a new clinical trial combining the anti-tumor activity of TMZ with an mTOR inhibitor. Recurrence as GBM was associated with aberrations to cell cycle genes through convergence of both genetic and epigenetic mechanisms. Moreover, we found that the evolutionary history of a tumor is similar whether inferred from genetic or epigenetic data, suggesting co-evolution of the genome and epigenome. Finally, we identified cases in which mutations in IDH1, which are the earliest known alteration in LGG and drive gliomagenesis, were either deleted or amplified at recurrence. Mutant IDH1 reprograms the epigenome and these recurrences showed partial reversion of these epigenomic alterations. Together, these findings highlight the heterogeneity and continual evolution of LGG and emphasize the importance of studying recurrent tumors for a more complete understanding of tumor evolution and to make more informed treatment decisions.