The loss of gamma-aminobutyric acid (GABA)-ergic medium spiny neurons (MSNs) in the striatum is the hallmark of Huntington disease (HD), an incurable neurodegenerative disorder characterized by progressive motor, psychiatric, and cognitive symptoms. Transplantation of MSNs or their precursors represents a promising treatment strategy for HD. In initial clinical trials in which HD patients received fetal neurografts directly into the striatum without a pretransplant cell-differentiation step, some patients exhibited temporary benefits. Meanwhile, major challenges related to graft overgrowth, insufficient survival of grafted cells, and limited availability of donated fetal tissue remain. Thus, the development of approaches that allow modeling of MSN differentiation and HD development in cell culture platforms may improve our understanding of HD and translate, ultimately, into HD treatment options. Here, recent advances in the in vitro differentiation of MSNs derived from fetal neural stem cells/progenitor cells (NSCs/NPCs), embryonic stem cells (ESCs), induced pluripotent stem cells (iPSCs), and induced NSCs (iNSCs) as well as advances in direct transdifferentiation are reviewed. Progress in non-allele specific and allele specific gene editing of HTT is presented as well. Cell characterization approaches involving phenotyping as well as in vitro and in vivo functional assays are also discussed.