One of the major Ca2+ signaling pathways is store-operated Ca2+ entry (SOCE), which is responsible for Ca2+ flow into cells in response to the depletion of endoplasmic reticulum Ca2+ stores. SOCE and its molecular components, including stromal interaction molecule proteins, Orai Ca2+ channels, and transient receptor potential canonical channels, are involved in the physiology of neural stem cells and play a role in their proliferation, differentiation, and neurogenesis. This suggests that Ca2+ signaling is an important player in brain development. Huntington’s disease (HD) is an incurable neurodegenerative disorder that is caused by polyglutamine expansion in the huntingtin (HTT) protein, characterized by the loss of γ-aminobutyric acid (GABA)-ergic medium spiny neurons (MSNs) in the striatum. However, recent research has shown that HD is also a neurodevelopmental disorder and Ca2+ signaling is dysregulated in HD. The relationship between HD pathology and elevations of SOCE was demonstrated in different cellular and mouse models of HD and in induced pluripotent stem cell-based GABAergic MSNs from juvenile- and adult-onset HD patient fibroblasts. The present review discusses the role of SOCE in the physiology of neural stem cells and its dysregulation in HD pathology. It has been shown that elevated expression of STIM2 underlying the excessive Ca2+ entry through store-operated calcium channels in induced pluripotent stem cell-based MSNs from juvenile-onset HD. In the light of the latest findings regarding the role of Ca2+ signaling in HD pathology we also summarize recent progress in the in vitro differentiation of MSNs that derive from different cell sources. We discuss advances in the application of established protocols to obtain MSNs from fetal neural stem cells/progenitor cells, embryonic stem cells, induced pluripotent stem cells, and induced neural stem cells and the application of transdifferentiation. We also present recent progress in establishing HD brain organoids and their potential use for examining HD pathology and its treatment. Moreover, the significance of stem cell therapy to restore normal neural cell function, including Ca2+ signaling in the central nervous system in HD patients will be considered. The transplantation of MSNs or their precursors remains a promising treatment strategy for HD.