In scientific research, the method is an indispensable means to solve scientific problems and a critical research object. With the advancement of sciences, many scientific methods are being proposed, modified, and used in academic literature. The authors describe details of the method in the abstract and body text, and key entities in academic literature reflecting names of the method are called method entities. Exploring diverse method entities in a tremendous amount of academic literature helps scholars understand existing methods, select the appropriate method for research tasks, and propose new methods.Furthermore, the evolution of method entities can reveal the development of a discipline and facilitate knowledge discovery. Therefore, this article offers a systematic review of methodological and empirical works focusing on extracting method entities from full-text academic literature and efforts to build knowledge services using these extracted method entities. Definitions of key concepts involved in this review were first proposed. Based on these definitions, we systematically reviewed the approaches and indicators to extract and evaluate method entities, with a strong focus on the pros and cons of each approach. We also surveyed how extracted method entities are used to build new applications. Finally, limitations in existing works as well as potential next steps were discussed.