This paper discusses the theory of concurrent processing in the context of the actor paradigm. The basic precepts of the actor paradigm are explained. We develop a new formalism to describe the behavior of actors and the evolution of systems of actors. It is hoped that the structure of concurrent computation and the intuitions behind the actor paradigm will be better understood in terms of this model. In particular, we define certain relations between the configurations an actor system may be in and explain how the behavior of actor systems can be understood in terms of these relations. We also define an actor-based language, called Sal, which has a simple syntax but nevertheless embodies the concepts involved. Several examples of simple actor systems are presented. Two kinds of actors are defined and their relevance to spawning concurrency is noted. The low level detail inherent in the transition systems we define retains some purely operational information. The usefulness of our constructs, beside the obvious pedagogic one, will be in the ability to abstract higher level principles to express and prove properties of actor systems, without the combinatorial explosion implied by all the possible inter-leavings of events. We suggest some directions for future research in this area.