The cellular response to the extracellular matrix (ECM) microenvironment mediated by integrin adhesion is of fundamental importance, in both developmental and pathological processes. In particular, mechanotransduction is of growing importance in groundbreaking cellular models such as induced pluripotent stem cells (iPSC), since this process may strongly influence cell fate and, thus, augment the precision of differentiation into specific cell types, e.g., cardiomyocytes. The decryption of the cellular machinery starting from ECM sensing to iPSC differentiation calls for new in vitro methods. Conveniently, engineered biomaterials activating controlled integrin-mediated responses through chemical, physical, and geometrical designs are key to resolving this issue and could foster clinical translation of optimized iPSC-based technology. This review introduces the main integrin-dependent mechanisms and signalling pathways involved in mechanotransduction. Special consideration is given to the integrin-iPSC linkage signalling chain in the cardiovascular field, focusing on biomaterial-based in vitro models to evaluate the relevance of this process in iPSC differentiation into cardiomyocytes.