We present several models of concurrent computation including process calculi, which belong to interleaving models, and events structures, which are an example of the so-called true concurrency models. A particular attention is paid to representing such phenomena as causality and conflict, and how they are represented in different models. We then introduce the notion of reversing a computation, discuss briefly its history, motivation, and list main application areas of reversible computation. We demonstrate that reversibility bridges a "gap" between the interleaving and true concurrency models. On the one hand we show that, for example, true concurrency equivalences can be characterised naturally by interleaving bisimulations or modal logics provided that we have reversibility in the interleaving model. On the other hand, we can talk directly about, for example, true concurrency's causality in the interleaving models again if we have reversibility. We look also at reachability in computation where processes execute both forwards and in reverse.