Experimental control over progenitor cell lineage specification can be achieved by modulating properties of the cell's microenvironment. These include physical properties of the cell adhesion substrate, such as rigidity, topography and deformation owing to dynamic mechanical forces. Multipotent mesenchymal stem cells (MSCs) generate contractile forces to sense and remodel their extracellular microenvironments and thereby obtain information that directs broad aspects of MSC function, including lineage specification. Various physical factors are important regulators of MSC function, but improved understanding of MSC mechanobiology requires novel experimental platforms. Engineers are bridging this gap by developing tools to control mechanical factors with improved precision and throughput, thereby enabling biological investigation of mechanics-driven MSC function. In this review, we introduce MSC mechanobiology and review emerging cell culture platforms that enable new insights into mechanobiological control of MSCs. Our main goals are to provide engineers and microtechnology developers with an up-to-date description of MSC mechanobiology that is relevant to the design of experimental platforms and to introduce biologists to these emerging platforms.