Although all biological systems must obey the laws of physics, specific examples of physical limitations on the performance of biological systems remain sparce. Bacterial motility is among the quantitatively best-understood biological behaviors, and it has long served as a model of how physics can help to understand bacterial ability to move and follow chemical gradients in the environment (chemotaxis). Using example of Escherichia coli, I will discuss how physical limits might have shaped the evolution of bacterial motility and of the chemotaxis system. Our recent work suggests that physical limitations on bacterial swimming, along with fitness tradeoffs associated with investment of limited cellular resources in motility, can be sufficient to quantitatively explain regulation of motility gene expression in both, laboratory model strains and natural isolates of E. coli. Moreover, hydrodynamics also determines performance of bacterial microswimmers that could be used for various biotherapeutic applications, and taking physics into account is important for their rational engineering.