The physiochemical stem cell microenvironment regulates the delicate balance between self-renewal and differentiation. The three-dimensional assembly of stem cells facilitates cellular interactions that promote morphogenesis, analogous to the multicellular, heterotypic tissue organization that accompanies embryogenesis. Therefore, expansion and differentiation of stem cells as multicellular aggregates provides a controlled platform for studying the biological and engineering principles underlying spatiotemporal morphogenesis and tissue patterning. Moreover, three-dimensional stem cell cultures are amenable to translational screening applications and therapies, which underscores the broad utility of scalable suspension cultures across laboratory and clinical scales. In this review, we discuss stem cell morphogenesis in the context of fundamental biophysical principles, including the three-dimensional modulation of adhesions, mechanics, and molecular transport and highlight the opportunities to employ stem cell spheroids for tissue modeling, bioprocessing, and regenerative therapies.