A character network is a graph extracted from a narrative, in which vertices represent characters and edges correspond to interactions between them. A number of narrative-related problems can be addressed automatically through the analysis of character networks, such as summarization, classification, or role detection. Character networks are particularly relevant when considering works of fictions (e.g. novels, plays, movies, TV series), as their exploitation allows developing information retrieval and recommendation systems. However, works of fiction possess specific properties making these tasks harder.This survey aims at presenting and organizing the scientific literature related to the extraction of character networks from works of fiction, as well as their analysis. We first describe the extraction process in a generic way, and explain how its constituting steps are implemented in practice, depending on the medium of the narrative, the goal of the network analysis, and other factors. We then review the descriptive tools used to characterize character networks, with a focus on the way they are interpreted in this context. We illustrate the relevance of character networks by also providing a review of applications derived from their analysis. Finally, we identify the limitations of the existing approaches, and the most promising perspectives.