The materials cells are made of are strikingly different from man-made materials. Metabolism keeps cells out of equilibrium. Motor proteins and energy-consuming polymerization drive shape changes and motion. In contrast to macroscopic machines, though, there is no clear distinction between the force generators and the structural elements. Rather, the force-generating motor proteins are mixed with the elementary building blocks of cell structure on a molecular scale. The composite ensemble presents a new type of active material which is at the focus of intense current research. Simple model systems have been used successfully in exploring fundamental phenomena. Theoretical models are extending conventional soft matter approaches, and pioneering studies strive to analyze the complex nonequilibrium dynamics of living cells.