Understanding self-replication from an information processing perspective is important because, among other things, it can shed light on molecular mechanisms of biological reproduction and on prebiotic chemical evolution. Intuition, biological knowledge, and early computational models of self-replication all suggested that self-replication is an inherently complex process. In this paper we describe recent computational studies that challenge this viewpoint. We summarize our recent work with cellular automata models of simple yet non-trivial self-replicating structures called unsheathed loops. For example, one unsheathed loop consists of only six components and requires only 20 rules to specify the local intercomponent interactions needed to bring about replication. The implication of this work is that, when viewed as an emergent property of numerous local, concurrent interactions between components, self-replicating systems can be substantially simpler than is generally recognized.