Climate change presents a profound global challenge, demanding accurate modeling and prediction to mitigate its impacts. Traditional climate models often struggle with the complexity and non-linearity of climate systems, limiting their ability to capture extreme events and dynamic feedback loops. Machine learning (ML) has emerged as a transformative tool, leveraging vast and diverse datasets to enhance climate modeling accuracy and provide actionable insights. This review explores the role of ML in advancing climate change modeling and prediction, focusing on key techniques such as supervised learning, unsupervised learning, deep learning, and reinforcement learning. We examine applications in extreme weather forecasting, greenhouse gas monitoring, renewable energy optimization, and regional downscaling of climate models. Despite its potential, ML faces challenges such as data biases, model interpretability, and high computational demands. By integrating ML with traditional approaches and fostering interdisciplinary collaboration, this technology can revolutionize climate science, offering innovative solutions for understanding and addressing the complexities of a changing climate.