Randomization-based Machine Learning methods for prediction are currently a hot topic in Artificial Intelligence, due to their excellent performance in many prediction problems, with a bounded computation time. The application of randomization-based approaches to renewable energy prediction problems has been massive in the last few years, including many different types of randomization-based approaches, their hybridization with other techniques and also the description of new versions of classical randomization-based algorithms, including deep and ensemble approaches. In this paper we review the most important characteristics of randomization-based machine learning approaches and their application to renewable energy prediction problems. We describe the most important methods and algorithms of this family of modeling methods, and perform a critical literature review, examining predic-