We first illustrate features of the actor model and a variety of component algebras and morphisms through a series of simple examples. We then define three semantic models for actor computation starting with a generalization to open systems of Clinger''s event diagram model, and forming two abstractions: interaction diagrams and interaction paths. An algebra is defined on each semantic domain with operations for parallel composition, hiding of internal actors, and renaming, and we show that component algebra laws hold. We use these models to provide semantics for descriptions of actor components based on actor theories and show that the semantics is a component algebra homomorphism.