Self-propelled, synthetic active matters that transduce chemical energy into mechanical motion are examples of biomimetic nonequilibrium systems. They are of great current interest, with potential applications in nanomachinery, nanoscale assembly, fluidics, and chemical/biochemical sensing. Many of the physical challenges associated with generating motility on the micro- and nanoscale have recently been overcome, leading to the first generation of autonomous motors and pumps on scales ranging from microns to nanometers. This perspective focuses on catalytically powered motile systems, outlining major advances to date in motor/pump design, propulsion mechanisms and directional control, and intermotor communications leading to collective behavior. We conclude by discussing the possible future directions, from the fundamental questions that remain to be addressed to the design principles required for useful applications.