The WHO 2007 glioma classification system (based primarily on tumour histology) resulted in considerable interobserver variability and substantial variation in patient survival within grades. Furthermore, few risk factors for glioma were known. Discoveries over the past decade have deepened our understanding of the molecular alterations underlying glioma and have led to the identification of numerous genetic risk factors. The advances in molecular characterization of glioma have reframed our understanding of its biology and led to the development of a new classification system for glioma. The WHO 2016 classification system comprises five glioma subtypes, categorized by both tumour morphology and molecular genetic information, which led to reduced misclassification and improved consistency of outcomes within glioma subtypes. To date, 25 risk loci for glioma have been identified and several rare inherited mutations that might cause glioma in some families have been discovered. This Review focuses on the two dominant trends in glioma science: the characterization of diagnostic and prognostic tumour markers and the identification of genetic and other risk factors. An overview of the many challenges still facing glioma researchers is also included.