Since the generation of induced pluripotent stem cells in 2006, cellular reprogramming has attracted increasing attention as a revolutionary strategy for cell replacement therapy. Recent advances have revealed that somatic cells can be directly converted into other mature cell types, which eliminates the risk of neoplasia and the generation of undesired cell types. Astrocytes become reactive and undergo proliferation, which hampers axon regeneration following injury, stroke, and neurodegenerative diseases. An emerging technique to directly reprogram astrocytes into induced neural stem cells (iNSCs) and induced neurons (iNs) by neural fate determinants brings potential hope to cell replacement therapy for the above neurological problems. Here, we discuss the development of direct reprogramming of various cell types into iNs and iNSCs, then detail astrocyte-derived iNSCs and iNs in vivo and in vitro. Finally, we highlight the unsolved challenges and opportunities for improvement.