Diffuse gliomas comprise a group of primary brain tumors that originate from glial (precursor) cells and present as a variety of malignancy grades which have in common that they grow by diffuse infiltration. This phenotype complicates treatment enormously as it precludes curative surgery and radiotherapy. Furthermore, diffusely infiltrating glioma cells often hide behind a functional blood-brain barrier, hampering delivery of systemically administered therapeutic and diagnostic compounds to the tumor cells. The present review addresses the biological mechanisms that underlie the diffuse infiltrative phenotype, knowledge of which may improve treatment strategies for this disastrous tumor type. The invasive phenotype is specific for glioma: most other brain tumor types, both primary and metastatic, grow as delineated lesions. Differences between the genetic make-up of glioma and that of other tumor types may therefore help to unravel molecular pathways, involved in diffuse infiltrative growth. One such difference concerns mutations in the NADP+-dependent isocitrate dehydrogenase (IDH1 and IDH2) genes, which occur in >80% of cases of low grade glioma and secondary glioblastoma. In this review we present a novel hypothesis which links IDH1 and IDH2 mutations to glutamate metabolism, possibly explaining the specific biological behavior of diffuse glioma.