During the last decades, concurrency theory successfully developed salient concepts to formally model and soundly reason about distributed and parallel systems. In practice, however, most attempts at analyzing large systems face severe complexity issues, especially state explosion, which prevents to exhaustively enumerate reachable state spaces. Compositionality is the most promising approach to fight state explosion. In this article, we focus on finite-state verification techniques for asynchronous message-passing systems, highlighting the existence of multiple, diverse compositional techniques such as: compositional model generation, semi-composition and projection, automatic generation of projection interfaces, formula-dependent model generation, and partial model checking. These approaches have been implemented in the framework of the CADP (Construction and Analysis of Distributed Processes) software toolbox and applied to large-scale, industrial systems. A key point is the ability to combine several compositional techniques, as no single technique is sufficient to address all kinds of systems.