A wide range of ordinary Description Logics (DLs) have been explored by considering collections of concept/role constructors, and types of terminologies, yielding an array of complexity results. Representation and reasoning with plans is a very important topic in AI, yet there has been very little work on finding and studying DL constructors for plan concepts. We start to remedy this problem here by considering Plan DLs where concept instances are sequences of action instances, and hence plan concepts can be viewed as analogues of formal languages, describing sets of strings. Inspired by the clasp system, we consider using regular-like expressions, obtaining a rich variety of Plan DLs based on combinations of regular-like expression constructors, including sequence (concatenation), alternation (union, disjunction), looping (Kleene star), conjunction (intersection), and complement. To model the important notion of concurrency, we also consider interleaving. We present results from the formal language literature which have immediate bearing on the complexity of DL-like reasoning tasks. However, we also focus on succinctness of representation, and on expressive power, issues first studied by Franz Baader for ordinary DLs.