Abstract: The living cell and many of its components as well as artificially energized mimics of motility are examples of active soft matter. An understanding of the individual and collective behavior of active particles is one of the grand challenges of nonequilibrium statistical physics, and holds the key to a physical grasp of the mechanics and statistics of living matter. In this colloquium, I will examine how one can use a number of simple ideas to construct nonequilibrium model systems that can self-propel at micro- and nano-scale, and study their collective properties.