Tumor metastasis is a complex phenomenon that poses significant challenges to current cancer therapeutics. While the biochemical signaling involved in promoting motile phenotypes is well understood, the role of biomechanical interactions has recently begun to be incorporated into models of tumor cell migration. Specifically, we propose the unjamming transition, adapted from physical paradigms describing the behavior of granular materials, to better discern the transition toward an invasive phenotype. In this review, we introduce the jamming transition broadly and narrow our discussion to the different modes of 3D tumor cell migration that arise. Then we discuss the mechanical interactions between tumor cells and their neighbors, along with the interactions between tumor cells and the surrounding extracellular matrix. We center our discussion on the interactions that induce a motile state or unjamming transition in these contexts. By considering the interplay between biochemical and biomechanical signaling in tumor cell migration, we can advance our understanding of biomechanical control in cancer metastasis.