The induced pluripotent stem cell (iPSC) technology has transformed in vitro research and holds great promise to advance regenerative medicine. iPSCs have the capacity for an almost unlimited expansion, are amenable to genetic engineering, and can be differentiated into most somatic cell types. iPSCs have been widely applied to model human development and diseases, perform drug screening, and develop cell therapies. In this review, we outline key developments in the iPSC field and highlight the immense versatility of the iPSC technology for in vitro modeling and therapeutic applications. We begin by discussing the pivotal discoveries that revealed the potential of a somatic cell nucleus for reprogramming and led to successful generation of iPSCs. We consider the molecular mechanisms and dynamics of somatic cell reprogramming as well as the numerous methods available to induce pluripotency. Subsequently, we discuss various iPSC-based cellular models, from mono-cultures of a single cell type to complex three-dimensional organoids, and how these models can be applied to elucidate the mechanisms of human development and diseases. We use examples of neurological disorders, coronavirus disease 2019 (COVID-19), and cancer to highlight the diversity of disease-specific phenotypes that can be modeled using iPSC-derived cells. We also consider how iPSC-derived cellular models can be used in high-throughput drug screening and drug toxicity studies. Finally, we discuss the process of developing autologous and allogeneic iPSC-based cell therapies and their potential to alleviate human diseases.