Invocation Specifications of an API library are types of specifications that are able to describe the legal invocation sequences of methods. Client code should follow descriptions of invocation specifications to call upon methods provided by API libraries. If this procedure is not followed, defects can be introduced into client code, and reduce its integrity. Because invocation specifications define the properties that are trustworthy for a software system, they play a central role in the research of trustworthy software and model checking; however, due to the great efforts to write invocation specifications, most API libraries do not provide such specifications. To address the problem, researchers have proposed various approaches to mine invocation specifications automatically. In this paper update-to-date research of mining specifications is surveyed, and the potential direction of further research is discussed.