Analogies with inert soft condensed matter--such as viscoelastic liquids, pastes, foams, emulsions, colloids, and polymers--can be used to investigate the mechanical response of soft biological tissues to forces. A variety of experimental techniques and biophysical models have exploited these analogies allowing the quantitative characterization of the mechanical properties of model tissues, such as surface tension, elasticity, and viscosity. The framework of soft matter has been successful in explaining a number of dynamical tissue behaviors observed in physiology and development, such as cell sorting, tissue spreading, or the escape of individual cells from a tumor. However, living tissues also exhibit active responses, such as rigidity sensing or cell pulsation, that are absent in inert soft materials. The soft matter models reviewed here have provided valuable insight in understanding morphogenesis and cancer invasion and have set bases for using tissue engineering within medicine.