Friction is a critical factor in the proper functioning of human organs as well as in the potential development of disease. It is also important for the design of diagnostic and interventional medical devices. Nanoscale surface roughness, viscoelastic or plastic deformations, wear, and lubrication all influence the functions of individual cells. The effects of friction in soft matter systems are quantified using different types of frictional coefficients, including: the dynamic friction coefficient; friction-skin drag; and pressure drag. These coefficients are determined by the viscoelastic properties of the two systems in contact and their relative velocity. In this review, several biological systems are considered, including: (i) epithelial tissues in contact with soft hydrogel-like implants; (ii) the collective migration of epithelial monolayers on substrate matrices; (iii) blood flow through blood vessels; and (iv) the movement of cancer cells past epithelial clusters along with the migration of epithelial cells within the cluster.