Active materials are composed of particles that can convert energy into autonomous motion. This renders them intrinsically far from equilibrium, resulting in rich dynamical and self-organizing behavior that defies the laws of conventional equilibrium statistical mechanics. Examples in nature are abundant and occur on all length scales, ranging from the cellular cytoskeleton to macroscopic bird flocking. Artificially created active particles have also recently become available, offering potential applications in bio-sensing and targeted drug delivery. We employ theory and particle-resolved computer simulations to study the emergent behavior of such active materials. In current research we explore the role of geometric and topological constraints, the emergence of mechanical stability, and aging and rejuvenation behavior in active matter.