Climate change is likely to profoundly modulate the burden of infectious diseases. However, attributing health impacts to a changing climate requires being able to associate changes in infectious disease incidence with the potentially complex influences of climate. This aim is further complicated by nonlinear feedbacks inherent in the dynamics of many infections, driven by the processes of immunity and transmission. Here, we detail the mechanisms by which climate drivers can shape infectious disease incidence, from direct effects on vector life history to indirect effects on human susceptibility, and detail the scope of variation available with which to probe these mechanisms. We review approaches used to evaluate and quantify associations between climate and infectious disease incidence, discuss the array of data available to tackle this question, and detail remaining challenges in understanding the implications of climate change for infectious disease incidence. We point to areas where synthesis between approaches used in climate science and infectious disease biology provide potential for progress.