In this talk, we present recent progress in understanding topological defects in liquid crystals, both conventional and active. We emphasize that topology is only one part of the theory of topological defects. Beyond topology, we need geometry to characterize the orientational properties of defects. We need energy and forces to understand the interactions between defects, and the conventional and active stimuli acting on them. Further, we need dynamics to understand the motion of defects under these forces, in the presence of dissipation. We discuss all of these aspects of the theory of defects in both two and three dimensions.