This article presents a review of the evolution of automatic post-editing, a term that describes methods to improve the output of machine translation systems, based on knowledge extracted from datasets that include post-edited content. The article describes the specificity of automatic post-editing in comparison with other tasks in machine translation, and it discusses how it may function as a complement to them. Particular detail is given in the article to the five-year period that covers the shared tasks presented in WMT conferences (2015–2019). In this period, discussion of automatic post-editing evolved from the definition of its main parameters to an announced demise, associated with the difficulties in improving output obtained by neural methods, which was then followed by renewed interest. The article debates the role and relevance of automatic post-editing, both as an academic endeavour and as a useful application in commercial workflows.