Cardiac organoids represent an important bioengineering opportunity in the development of models to study human heart pathophysiology. By incorporating multiple cardiac cell types in three-dimensional culture and developmentally-guided biochemical signaling, cardiac organoids recapitulate numerous features of heart tissue. However, cardiac tissue also experiences a variety of mechanical forces as the heart develops and over the course of each contraction cycle. It is now clear that these forces impact cellular specification, phenotype, and function, and should be incorporated into the engineering of cardiac organoids in order to generate better models. In this review, we discuss strategies for engineering cardiac organoids and report the effects of organoid design on the function of cardiac cells. We then discuss the mechanical environment of the heart, including forces arising from tissue elasticity, contraction, blood flow, and stretch, and report on efforts to mimic these biophysical cues in cardiac organoids. Finally, we review emerging areas of cardiac organoid research, for the study of cardiac development, the formation of multi-organ models, and the simulation of the effects of spaceflight on cardiac tissue and consider how these investigations might benefit from the inclusion of mechanical cues.