In this paper, we performed an analysis of the 500 most relevant scientific articles published since 2018, concerning machine learning methods in the field of climate and numerical weather prediction using the Google Scholar search engine. The most common topics of interest in the abstracts were identified, and some of them examined in detail: in numerical weather prediction research—photovoltaic and wind energy, atmospheric physics and processes; in climate research—parametrizations, extreme events, and climate change. With the created database, it was also possible to extract the most commonly examined meteorological fields (wind, precipitation, temperature, pressure, and radiation), methods (Deep Learning, Random Forest, Artificial Neural Networks, Support Vector Machine, and XGBoost), and countries (China, USA, Australia, India, and Germany) in these topics. Performing critical reviews of the literature, authors are trying to predict the future research direction of these fields, with the main conclusion being that machine learning methods will be a key feature in future weather forecasting.