Diffusely infiltrating gliomas are the most common primary brain tumors and include astrocytomas, oligodendrogliomas, and oligoastrocytomas of grades II and III and glioblastoma (GBM), grade IV. Histologic classification is increasingly aided by molecular genetic studies, which assist in the diagnosis and provide prognostic and predictive value. Mutations in IDH1 are frequent in grades II and III astrocytomas, oligodendrogliomas, and oligoastrocytomas, as well as secondary GBMs. IDH1-mutated diffuse gliomas are distinct from their IDH1 wild-type counterparts based on clinical features, growth rates, and concurrent genomic alterations. Grades II and III astrocytomas, as well as secondary GBMs are characterized by IDH1, TP53, and ATRX mutations, whereas oligodendrogliomas most frequently harbor codeletion of 1p/19q and mutations in CIC, FUBP1, and the TERT promoter. Primary GBMs frequently show molecular alterations in EGFR, PDGFRA, PTEN, TP53, NF1, and CDKN2A/B, as well as TERT promoter mutations, but not IDH mutations. Pediatric GBMs have a distinctive molecular pathogenesis, as H3F3A and DAXX mutations are frequent, and their gene expression profile is different than adult GBMs. Other lower-grade gliomas of childhood, such as pilocytic astrocytoma and pleomorphic xanthoastrocytoma, are characterized by BRAF mutations or activating gene rearrangements involving BRAF.