Application programming interface (API) is an important form of software reuse. API documentations, such as API specifications, tutorials, and online forums, are valuable learning resources for reusing the APIs. In recent years, many data-driven API documentation mining (ADM) methods have been proposed. These methods mine API documentations and return API-related information to help developers better understand and reuse APIs. These methods treat documentations as unstructured data and apply various data mining techniques to analyze the documentation data. Currently, there is no comprehensive review of the data-driven approach to API documentation mining. This review aims to fill in this gap by analyzing and discussing the state of the art ADM papers. We survey 32 representative papers published in prominent software engineering journals and conferences in recent 5 years (January 2014-July 2019). We analyze their mining tasks, mined data, problems, data mining techniques, and evaluation metrics. Based on the survey results, we point out research challenges and future research directions in this area.