Climate change represents one of the most significant challenges faced today, requiring innovative and efficient strategies to mitigate its effects and adapt to changing environmental circumstances. In response, quantum machine learning (QML) has surfaced as an exciting interdisciplinary domain. By leveraging the computational benefits of quantum computing along with the predictive capabilities of machine learning, QML presents encouraging novel methods for addressing intricate climate-related issues. Climate science, with its complex, high-dimensional data and urgent need for actionable insights, presents a promising application domain for QML. QML has the potential to change climate science by making data analysis faster, improving climate models, and giving better predictions about climate change. QML tries to find new solutions to big climate problems like risk assessment, disaster planning, and reducing carbon emissions. This chapter provides a comprehensive overview of climate science fundamentals, reviews major QML techniques applied in climate science, and explores the synergies between quantum computing and machine learning in advancing sustainable climate solutions.