Process mining (PM) aims at discovering, monitoring and improving real processes by obtaining knowledge from event logs. It has been used in a variety of fields and has gained attention due to its ability to optimise processes, detect bottlenecks and reduce costs. In this article we provide a concise overview of process mining applied in the healthcare sector, which due to its inner complexity represents a challenge. The contribution of the article is two-fold: First, we present the results of a thorough review of the PM literature applied to the healthcare domain. We do not explain all papers in detail, on the contrary, we discuss current trends along nine dimensions of PM, namely Objective, Type, Perspective, Algorithms & Tools, Medical facilities, Medical fields, Medical process type, Medical data, and Preprocessing. By doing so, this article serves as an introductory reference for researchers interested in this field. Second, we discuss the main challenges of PM applied to the healthcare domain and point out several research lines that remain open.