Low-grade gliomas represent the most frequent primary brain tumors in children, and are also an important category of brain neoplasms in young adults. They are characterized by slow growth, but often associated with increased morbidity, as well as mortality in the subset that develop histologic progression. Pathologically they correspond to WHO grade I or II and include pilocytic astrocytoma (PA), pilomyxoid astrocytoma variant, angiocentric glioma, diffuse astrocytoma, oligodendroglioma, oligoastrocytoma, and pleomorphic xanthoastrocytoma (PXA). Although all low-grade glioma subtypes may develop in children and adults, and be histologically indistinguishable in these two populations, there are important clinical and molecular differences. As a rule, low-grade gliomas in adults have a greater tendency for histologic progression and more aggressive clinical behavior than those in children. With respect to genetic alterations, activating BRAF alterations and increased MAPK pathway signaling are near universal features of the circumscribed low-grade glioma group (e.g., PA and PXA). Whole exome/genome sequencing efforts and high resolution copy number platforms have also provided important biologic insights in these tumors, with adult low-grade diffuse gliomas containing frequent ATRX, TP53 mutations (astrocytomas), as well as 1p19q co-deletions, CIC, FUBP1 and TERT promoter mutations (oligodendrogliomas). Conversely, alterations in FGFR1, MYB, and MYBL1 are frequent events in pediatric low-grade diffuse gliomas. In this review we summarize our current knowledge of the diagnostic and molecular pathology of these tumors, and explore possible avenues for targeted therapeutics.