The global trend toward a green sustainable future encouraged the penetration of renewable energies into the electricity sector to satisfy various demands of the market. Successful and steady integrations of renewables into the microgrids necessitate building reliable, accurate wind and solar power forecasters adopting these renewables' stochastic behaviors. In a few reported literature studies, machine learning- (ML-) based forecasters have been widely utilized for wind power and solar power forecasting with promising and accurate results. The objective of this article is to provide a critical systematic review of existing wind power and solar power ML forecasters, namely artificial neural networks (ANNs), recurrent neural networks (RNNs), support vector machines (SVMs), and extreme learning machines (ELMs). In addition, special attention is paid to metaheuristics accompanied by these ML models. Detailed comparisons of the different ML methodologies and the metaheuristic techniques are performed. The significant drawn-out findings from the reviewed papers are also summarized based on the forecasting targets and horizons in tables. Finally, challenges and future directions for research on the ML solar and wind prediction methods are presented. This review can guide scientists and engineers in analyzing and selecting the appropriate prediction approaches based on the different circumstances and applications.