Studies of the pathogenic mechanisms underlying human myopathies and muscular dystrophies often require animal models, but models of some human diseases are not yet available. The present invention provides methods to promote the engraftment and development of myogenic cells from individuals with such diseases into mature muscle tissue in mice to treat muscle diseases, muscle injury and reduced muscle function. Immortalized human myogenic precursor cells (hMPCs) form mature human myofibers following implantation into the hindlimbs of immunodeficient mice. The engraftment of the cells and their development into mature muscle myofibers is promoted by intermittent neuromuscular electrical stimulation (iNMES) of the peroneal nerve of the engrafted limb. The human myofibers that form are innervated, their contractile apparatus is fully differentiated, and they are comprised of human myonuclei, with minimal contamination by murine myonuclei.