This article discusses the integration of machine learning (ML) with climate physics and simulations, highlighting the use of ML techniques to accelerate climate research. It outlines two main areas: ML for climate physics and ML for climate simulations. ML-based models, such as neural networks, have shown success in weather forecasting but face challenges in the small-data, non-stationary regime, where physics knowledge is crucial for generalizability. Climate projections involve non-stationarity, making ML models less effective without incorporating physics constraints. The article emphasizes the need for collaboration between climate physics, ML theory, and numerical analysis to develop reliable ML-based models for climate applications. ML techniques are used to extract knowledge from climate data, including dimensionality reduction, supervised and unsupervised learning, and equation discovery. These methods help identify patterns, discover predictive models, and improve the accuracy of climate simulations. Equation discovery, for example, has been used to derive closed-form equations for climate processes, enhancing interpretability. ML-based parameterizations, such as subgrid-scale (SGS) parameterizations, are also being developed to improve the accuracy of climate models. Climate simulations benefit from ML emulators, which can generate large ensembles of simulations at a fraction of the computational cost of physics-based models. These emulators, trained on high-resolution simulations or observations, can predict climate responses to different emission scenarios. However, challenges remain in ensuring the physical consistency and stability of ML-based models, particularly in the small-data regime. Incorporating physics constraints, such as conservation laws and symmetries, helps address these challenges and improves the reliability of ML-based climate models. The article concludes that while ML offers promising opportunities for climate science, significant challenges remain in ensuring the physical accuracy and reliability of ML-based models.This article discusses the integration of machine learning (ML) with climate physics and simulations, highlighting the use of ML techniques to accelerate climate research. It outlines two main areas: ML for climate physics and ML for climate simulations. ML-based models, such as neural networks, have shown success in weather forecasting but face challenges in the small-data, non-stationary regime, where physics knowledge is crucial for generalizability. Climate projections involve non-stationarity, making ML models less effective without incorporating physics constraints. The article emphasizes the need for collaboration between climate physics, ML theory, and numerical analysis to develop reliable ML-based models for climate applications. ML techniques are used to extract knowledge from climate data, including dimensionality reduction, supervised and unsupervised learning, and equation discovery. These methods help identify patterns, discover predictive models, and improve the accuracy of climate simulations. Equation discovery, for example, has been used to derive closed-form equations for climate processes, enhancing interpretability. ML-based parameterizations, such as subgrid-scale (SGS) parameterizations, are also being developed to improve the accuracy of climate models. Climate simulations benefit from ML emulators, which can generate large ensembles of simulations at a fraction of the computational cost of physics-based models. These emulators, trained on high-resolution simulations or observations, can predict climate responses to different emission scenarios. However, challenges remain in ensuring the physical consistency and stability of ML-based models, particularly in the small-data regime. Incorporating physics constraints, such as conservation laws and symmetries, helps address these challenges and improves the reliability of ML-based climate models. The article concludes that while ML offers promising opportunities for climate science, significant challenges remain in ensuring the physical accuracy and reliability of ML-based models.