Multilayer networks have been widely used to represent and analyze systems of interconnected entities where both the entities and their connections can be of different types. However, real multilayer networks can be difficult to analyze because of irrelevant information, such as layers not related to the objective of the analysis, because of their size, or because traditional methods defined to analyze simple networks do not have a straightforward extension able to handle multiple layers. Therefore, a number of methods have been devised in the literature to simplify multilayer networks with the objective of improving our ability to analyze them. In this article we provide a unified and practical taxonomy of existing simplification approaches, and we identify categories of multilayer network simplification methods that are still underdeveloped, as well as emerging trends.