Term rewriting is a simple, yet expressive model of computation, which finds direct applications in specification and programming languages (many of which embody rewrite rules, pattern matching, and abstract data types), but also indirect applications, e.g., to express the semantics of data types or concurrent processes, to specify program transformations, to perform computer-aided verification, etc. The Rewrite Engines Competition (REC) was created under the aegis of the Workshop on Rewriting Logic and its Applications (WRLA) to serve three main goals: (i) being a forum in which tool developers and potential users of term rewrite engines can share experience; (ii) bringing together the various language features and implementation techniques used for term rewriting; and (iii) comparing the available term rewriting languages and tools in their common features. The present article provides a retrospective overview of the four editions of the Rewrite Engines Competition (2008, 2010, and 2018) and traces their evolution over time.