In the developing brain, the three major cell types, i.e., neurons, astrocytes and oligodendrocytes, are generated from common multipotent neural stem cells (NSCs). In particular, astrocytes eventually occupy a great fraction of the brain and play pivotal roles in the brain development and functions. However, NSCs cannot produce the three major cell types simultaneously from the beginning; e.g., it is known that neurogenesis precedes astrogenesis during brain development. How is this fate switching achieved? Many studies have revealed that extracellular cues and intracellular programs are involved in the transition of NSC fate specification. The former include growth factor- and cytokine-signaling, and the latter involve epigenetic machinery, including DNA methylation, histone modifications, and non-coding RNAs. Accumulating evidence has identified a complex array of epigenetic modifications that control the timing of astrocytic differentiation of NSCs. In this review, we introduce recent progress in identifying the molecular mechanisms of astrogenesis underlying the tight regulation of neuronal-astrocytic fate switching of NSCs.