Cancer comprises a large group of complex diseases which arise from the misrouted interplay of mutated cells with other cells and the extracellular matrix. The extracellular matrix is a highly dynamic structure providing biochemical and biophysical cues that regulate tumor cell behavior. While the relevance of biochemical signals has been appreciated, the complex input of biophysical properties like the variation of ligand density and distribution is a relatively new field in cancer research. Nanotechnology has become a very promising tool to mimic the physiological dimension of biophysical signals and their positive (i.e., growth-promoting) and negative (i.e., anti-tumoral or cytotoxic) effects on cellular functions. Here, we review tumor-associated cellular functions such as proliferation, epithelial-mesenchymal transition (EMT), invasion, and phenotype switch that are regulated by biophysical parameters such as ligand density or substrate elasticity. We also address the question of how such factors exert inhibitory or even toxic effects upon tumor cells. We describe three principles of nanostructured model systems based on block copolymer nanolithography, electron beam lithography, and DNA origami that have contributed to our understanding of how biophysical signals direct cancer cell fate.