Optical character recognition (OCR) is one of the most popular techniques used for converting printed documents into machine-readable ones. While OCR engines can do well with modern text, their performance is unfortunately significantly reduced on historical materials. Additionally, many texts have already been processed by various out-of-date digitisation techniques. As a consequence, digitised texts are noisy and need to be post-corrected. This article clarifies the importance of enhancing quality of OCR results by studying their effects on information retrieval and natural language processing applications. We then define the post-OCR processing problem, illustrate its typical pipeline, and review the state-of-the-art post-OCR processing approaches. Evaluation metrics, accessible datasets, language resources, and useful toolkits are also reported. Furthermore, the work identifies the current trend and outlines some research directions of this field.