The importance of the tumor microenvironment in cancer progression is indisputable, yet a key component of the microenvironment--biomechanical forces--remains poorly understood. Tumor growth and progression is paralleled by a host of physical changes in the tumor microenvironment, such as growth-induced solid stresses, increased matrix stiffness, high fluid pressure, and increased interstitial flow. These changes to the biomechanical microenvironment promote tumorigenesis and tumor cell invasion and induce stromal cells--such as fibroblasts, immune cells, and endothelial cells--to change behavior and support cancer progression. This review highlights what we currently know about the biomechanical forces generated in the tumor microenvironment, how they arise, and how these forces can dramatically influence cell behavior, drawing not only upon studies directly related to cancer and tumor cells, but also work in other fields that have shown the effects of these types of mechanical forces vis-à-vis cell behaviors relevant to the tumor microenvironment. By understanding how all of these biomechanical forces can affect tumor cells, stromal cells, and tumor-stromal crosstalk, as well as alter how tumor and stromal cells perceive other extracellular signals in the tumor microenvironment, we can develop new approaches for diagnosis, prognosis, and ultimately treatment of cancer.