Huntington’s disease (HD) is an inherited, autosomal dominant, degenerative disease characterized by involuntary movements, cognitive decline, and behavioral impairment ending in death. HD is caused by an expansion in the number of CAG repeats in the huntingtin gene on chromosome 4. To date, no effective therapy for preventing the onset or progression of the disease has been found, and many symptoms do not respond to pharmacologic treatment. However, recent results of pre-clinical trials suggest a beneficial effect of stem-cell-based therapy. Induced pluripotent stem cells (iPSCs) represent an unlimited cell source and are the most suitable among the various types of autologous stem cells due to their patient specificity and ability to differentiate into a variety of cell types both in vitro and in vivo. Furthermore, the cultivation of iPSC-derived neural cells offers the possibility of studying the etiopathology of neurodegenerative diseases, such as HD. Moreover, differentiated neural cells can organize into three-dimensional (3D) organoids, mimicking the complex architecture of the brain. In this article, we present a comprehensive review of recent HD models, the methods for differentiating HD–iPSCs into the desired neural cell types, and the progress in gene editing techniques leading toward stem-cell-based therapy.