and biochemical approaches [@leber2009molecular; @hanahan2000hallmarks; @hanahan2011hallmarks]. However, the physical aspects of metastatic invasion are still unclear [@hanahan2011hallmarks]. We know that at a fundamental level, metastatic invasion is a physical process. Tumor cells sense and respond to chemical gradients provided by surrounding cells [@bhowmick2004stromal; @condeelis2006macrophages; @shields2007autologous; @puliafito2015three] or other features of the tumor environment [@shields2007autologous; @polacheck2011interstitial; @shieh2011regulation] (Fig. \[overview\]A). Indeed, tumor cells are highly sensitive, able to detect a $1\%$ difference in concentration across the cell length [@shields2007autologous]. Sensing is ultimately a physical phenomenon. Therefore, can we build a simple physical theory to understand the sensory behavior of tumor cells, and can this physical theory inform treatment options?

Metastatic invasion involves coordinated migration of tumor cells away from the tumor site. In many types of cancer, migration is collective and highly organized, involving the coherent motion of connected groups of cells [@cheung2013collective; @friedl2012classifying; @aceto2014circulating; @puliafito2015three] (Fig. \[overview\]B). Collective migration is ultimately a physical phenomenon, since it relies on mechanical coupling and can often be understood as emerging from simple physical interactions at the cell-to-cell level. Can we understand the collective migration of tumor cells with simple physical models?

Here we review recent progress on modeling sensing and migration in cells and 