Extreme weather events pose significant challenges, thereby demanding techniques for accurate analysis and precise forecasting to mitigate its impact. In recent years, deep learning techniques have emerged as a promising approach for weather forecasting and understanding the dynamics of extreme weather events. This review aims to provide a comprehensive overview of the state-of-the-art deep learning in the field. We explore the utilization of deep learning architectures, across various aspects of weather prediction such as thunderstorm, lightning, precipitation, drought, heatwave, cold waves and tropical cyclones. We highlight the potential of deep learning, such as its ability to capture complex patterns and non-linear relationships. Additionally, we discuss the limitations of current approaches and highlight future directions for advancements in the field of meteorology. The insights gained from this systematic review are crucial for the scientific community to make informed decisions and mitigate the impacts of extreme weather events.