Yes-associated protein (YAP) and WW domain-containing transcription regulator protein 1 (WWTR1, also known as TAZ) are transcriptional coactivators in the Hippo signaling pathway. Both are well-known regulators of cell proliferation and organ size control, and they have significant roles in promoting cell proliferation and differentiation. The roles of YAP and TAZ in stem cell pluripotency and differentiation have been extensively studied. However, the upstream mediators of YAP and TAZ are not well understood. Recently, a novel role of YAP in mechanosensing and mechanotransduction has been reported. The present review updates information on the regulation of YAP by mechanical cues such as extracellular matrix stiffness, fluid shear stress, and actin cytoskeleton tension in stem cell behaviors and differentiation. The review explores mesenchymal stem cell fate decisions, pluripotent stem cells (PSCs), self-renewal, pluripotency, and differentiation to blood products. Understanding how cells sense their microenvironment or niche and mimic those microenvironments in vitro could improve the efficiency of producing stem cell products and the efficacy of the products.