Climate change is one of the most important issues facing the world today; precise climate modelling is crucial for forecasting its effects, directing adaptation plans, and influencing policies. Despite their scientific rigour, traditional climate models frequently have drawbacks, such as high computational costs, coarse temporal and spatial resolutions, and difficulties accurately representing complex nonlinear processes. By facilitating the identification of hidden patterns, increasing predictive accuracy, and accelerating simulation processes, artificial intelligence (AI) has recently surfaced as a promising tool to supplement and extend traditional approaches. This manuscript reviews the current use of AI for climate change modelling, focusing primarily on machine learning, deep learning, and hybrid AI approaches for diverse tasks. Several previous studies indicate that AI-driven models can improve seasonal forecasting, enhance extreme weather event projections, and optimise resources and energy management in light of climate change. Despite these advancements, numerous challenges remain. Limited data availability and quality frequently characterise climate change-related studies, significantly impacting the reliability of AI models. Furthermore, issues with computational scalability, uncertainty quantification, and integration with physical climate models continue to constrain widespread adoption. Future work must concentrate on improving surrogate modelling techniques, building strong AI-driven early warning systems for climate-related disasters, and creating hybrid frameworks that combine AI and physical models to fill these gaps.