Tissue engineering has developed many paradigms and techniques on how to best integrate cells and extracellular matrix to create in vitro structures that replicate native tissue. The strategy best suited for building these constructs depends mainly on the target cells, tissues, and organ of interest, and how readily their respective niches can be recapitulated in vitro with available technologies. In this review we examine engineered heart tissue and two techniques that can be used to induce tissue morphogenesis in artificial niches in vitro: engineered surface topology and electrical control of the system. For both the differentiation of stem cells into heart cells and further assembly of these cells into engineered tissues, these two techniques are effective in inducing in vivo like structure and function. Biophysical modulation through the control of topography and manipulation of the electrical microenvironment has been shown to have effects on cell growth and differentiation, expression of mature cardiac-related proteins and genes, cell alignment via cytoskeletal organization, and electrical and contractile properties. Lastly, we discuss the evolution and potential of these techniques, and bridges to regenerative therapies.