Accurate weather forecasting is essential for agriculture, disaster management, aviation, and climate monitoring. Traditional numerical weather prediction (NWP) models rely on physics-based equations that require high computational resources and often struggle with nonlinear atmospheric dynamics. In recent years, artificial intelligence (AI), particularly neural networks, has emerged as a powerful alternative for predictive weather modelling. This paper presents a comprehensive study of AI-based predictive weather modelling using neural networks, including Artificial Neural Networks (ANN), Convolutional Neural Networks (CNN), Long Short-Term Memory networks (LSTM), and Transformer architectures. A hybrid CNN–LSTM framework is proposed for spatiotemporal forecasting of meteorological variables. The system integrates satellite data, ground sensor inputs, and historical climate datasets. Experimental studies reported in literature demonstrate improved accuracy, reduced computational time, and better adaptability compared to traditional forecasting systems. The paper also discusses limitations, challenges, and future directions for real-time AI-driven weather prediction systems.