What does it mean to call something complex? This Review essay describes three recent books which take up complex problems and the problem of complexity: philosopher Angela Potochnik’s Idealization and the Aims of Science (2017); science and technology studies (STS) scholar Nicole Nelson’s Model Behavior: Animal Experiments, Complexity, and the Genetics of Psychiatric Disorders (2018); and historian of science Bruno Strasser’s Collecting Experiments: Making Big Data Biology (2019). Taken together, these works lay out a refreshed analytic vocabulary and set of guiding concerns for thinking about what complexity is and does in medical research, and how complexity mediates public participation in science and medicine.