Organoids have revolutionized the field of biomedical research by allowing the recapitulation of organ architecture in three dimensions. Though biochemical factors have long played an established role in organoid culture, it is presently recognized that mechanical forces are equally indispensable in the self-organization of tissues and the determination of stem cell and disease phenotypes. Here, this review integrates the biophysics of cellular mechanotransduction with the biology of organoid systems, examining how forces encoded in extracellular matrix stiffness, viscoelasticity, fluid shear, cyclic stretch, and geometric confinement are sensed and transduced by a specialized molecular machinery—including integrin–focal adhesion kinase (FAK) complexes, mechanosensitive Piezo1/2 ion channels, and the linker of nucleoskeleton and cytoskeleton (LINC) complex—to ultimately regulate Yes-associated protein/transcriptional coactivator with PDZ-binding motif (YAP/TAZ)-mediated transcriptional programs. How engineered hydrogels with tunable mechanical properties, microfluidic organ-on-chip platforms, and bioreactor systems have enabled in-depth exploration of these forces in gut, brain, cardiac, and kidney organoids will be well discussed. Emerging work highlights Piezo channels as critical gatekeepers of intestinal stem cell (ISC) fate, extracellular matrix (ECM) stiffness as a driver of aberrant gyrification in lissencephaly brain organoids, and viscoelastic stress relaxation as a key determinant of neural progenitor maturation. Organoid mechanobiology is set to revolutionize human disease modeling and regenerative medicine with its convergence with patient-derived models, computational mechanics, and Good Manufacturing Practice (GMP)-compatible bioengineering platforms.