Machine Learning (ML) force fields (ML-FFs) aim to bridge the gap between the accuracy of ab initio methods and the efficiency of classical force fields (FFs). By learning the statistical relationship between chemical structure and potential energy, ML-FFs can model complex interactions without relying on predefined bonding patterns or interaction knowledge. These models are limited only by the quality and quantity of reference data used for training. This review discusses the construction and application of ML-FFs, highlighting their ability to provide insights into chemical processes, including electronic effects, thermodynamics, reactions, nuclear quantum effects, and excited states. The text outlines the core concepts of ML-FFs, provides a step-by-step guide for their construction and testing, and discusses challenges such as locality and smoothness assumptions, transferability, scalability, and long-range interactions. It also covers physical and chemical insights gained from ML-FFs, including their ability to model nuclear quantum effects and excited states. The review concludes with a discussion of the remaining challenges in extending the applicability of ML-FFs. ML methods, including kernel-based learning and artificial neural networks, are reviewed for their role in constructing ML-FFs. These methods allow for efficient prediction of molecular properties and enable the modeling of complex systems with high accuracy. The review emphasizes the importance of invariances in physical systems and the need for ML models to respect these invariances to ensure physically meaningful predictions. The text also discusses the use of ML in molecular simulations, including the prediction of molecular wave functions and the integration of ML with traditional semi-empirical methods. Overall, ML-FFs offer a promising approach to studying chemical systems with both high accuracy and computational efficiency.Machine Learning (ML) force fields (ML-FFs) aim to bridge the gap between the accuracy of ab initio methods and the efficiency of classical force fields (FFs). By learning the statistical relationship between chemical structure and potential energy, ML-FFs can model complex interactions without relying on predefined bonding patterns or interaction knowledge. These models are limited only by the quality and quantity of reference data used for training. This review discusses the construction and application of ML-FFs, highlighting their ability to provide insights into chemical processes, including electronic effects, thermodynamics, reactions, nuclear quantum effects, and excited states. The text outlines the core concepts of ML-FFs, provides a step-by-step guide for their construction and testing, and discusses challenges such as locality and smoothness assumptions, transferability, scalability, and long-range interactions. It also covers physical and chemical insights gained from ML-FFs, including their ability to model nuclear quantum effects and excited states. The review concludes with a discussion of the remaining challenges in extending the applicability of ML-FFs. ML methods, including kernel-based learning and artificial neural networks, are reviewed for their role in constructing ML-FFs. These methods allow for efficient prediction of molecular properties and enable the modeling of complex systems with high accuracy. The review emphasizes the importance of invariances in physical systems and the need for ML models to respect these invariances to ensure physically meaningful predictions. The text also discusses the use of ML in molecular simulations, including the prediction of molecular wave functions and the integration of ML with traditional semi-empirical methods. Overall, ML-FFs offer a promising approach to studying chemical systems with both high accuracy and computational efficiency.