Intense precipitation events pose a significant threat to human life. Mathematical and computational models have been developed to simulate atmospheric dynamics to predict and understand these climates and weather events. However, recent advancements in artificial intelligence (AI) algorithms, particularly in machine learning (ML) techniques, coupled with increasing computer processing power and meteorological data availability, have enabled the development of more cost-effective and robust computational models that are capable of predicting precipitation types and aiding decision-making to mitigate damage. In this paper, we provide a comprehensive overview of the state-of-the-art in predicting precipitation events, addressing issues and foundations, physical origins of rainfall, potential use of AI as a predictive tool for forecasting, and computational challenges in this area of research. Through this review, we aim to contribute to a deeper understanding of precipitation formation and forecasting aided by ML algorithms.