Healthy skeletal muscle possesses the extraordinary ability to regenerate in response to small-scale injuries; however, this self-repair capacity becomes overwhelmed with aging, genetic myopathies, and large muscle loss. The failure of small animal models to accurately replicate human muscle disease, injury and to predict clinically-relevant drug responses has driven the development of high fidelity in vitro skeletal muscle models. Herein, the progress made and challenges ahead in engineering biomimetic human skeletal muscle tissues that can recapitulate muscle development, genetic diseases, regeneration, and drug response is discussed. Bioengineering approaches used to improve engineered muscle structure and function as well as the functionality of satellite cells to allow modeling muscle regeneration in vitro are also highlighted. Next, a historical overview on the generation of skeletal muscle cells and tissues from human pluripotent stem cells, and a discussion on the potential of these approaches to model and treat genetic diseases such as Duchenne muscular dystrophy, is provided. Finally, the need to integrate multiorgan microphysiological systems to generate improved drug discovery technologies with the potential to complement or supersede current preclinical animal models of muscle disease is described.