Classification problems and their corresponding solving approaches constitute one of the fields of machine learning. The application of classification schemes in Renewable Energy (RE) has gained significant attention in the last few years, contributing to the deployment, management and optimization of RE systems. The main objective of this paper is to review the most important classification algorithms applied to RE problems, including both classical and novel algorithms. The paper also provides a comprehensive literature review and discussion on different classification techniques in specific RE problems, including wind speed/power prediction, fault diagnosis in RE systems, power quality disturbance classification and other applications in alternative RE systems. In this way, the paper describes classification techniques and metrics applied to RE problems, thus being useful both for researchers dealing with this kind of problem and for practitioners of the field.