Materials can be endowed with unique properties by the integration of molecular motors. Molecular motors can have a biological origin or can be chemically synthesized and produce work from chemical energy or light. Their ability to access large internal or external reservoirs of energy enables a wide range of nonequilibrium behaviors, including the production of force, changes in shape, internal reorganization, and dynamic changes in mechanical properties—muscle tissue is one illustration of the possibilities. Current research efforts advance our experimental capabilities to create such “active matter” by using either biomolecular or synthetic motors, and also advance our theoretical understanding of these materials systems. Here, we introduce this exciting research field and highlight a few of the recent advances as well as open questions.