Forecasting the weather is a demanding endeavour for all scientists studying meteorology and the weather bureau. Numerous methods have been developed over the years to predict atmospheric conditions. Traditionally, methods like pattern recognition, synoptic forecasts, statistical forecasts, etc., were used to predict the weather, but they did not always yield promising results. In recent years, traditional methods of weather prediction have seen a transformative shift with the integration of Machine Learning (ML). The integration of meteorology with advanced data analytics has the potential to greatly improve the accuracy and reliability of weather forecasts. On reviewing several papers, we have found that using ML techniques weather can be more accurately predicted. This review offers a chronological overview of the evolution of ML applications in weather and climate modelling, tracing developments from early studies to the most recent advancements. It also provides a concise explanation of key ML concepts, methodologies, and ethical considerations. Additionally, the review explores promising directions for future research, aiming to serve as a foundational guide for researchers and model developers seeking to quickly acquaint themselves with ML’s role in weather and climate modelling.