This review article presents a comprehensive overview of data-driven (DD) techniques for discovering, encoding, surrogate, or emulating constitutive laws (CLs) that describe the path-independent and path-dependent response of solids. The objective is to provide a structured taxonomy of methodologies developed over the past decades, discussing the benefits and drawbacks of various techniques for interpreting and forecasting mechanics behavior across different scales. The article distinguishes between machine learning (ML)-based and model-free methods, categorizing approaches based on their interpretability and learning process, while addressing key challenges such as generalization and trustworthiness. It also discusses data sampling techniques, design of experiments, verification, and validation. The article begins by explaining the fundamental equations in solid mechanics, including conservation principles, kinematics, and constitutive laws. It highlights the traditional empirical nature of material modeling and the shift from limited to large-data regimes due to advances in experimental and computational methods. The review then classifies DD approaches into ML-based and model-free methods, discussing their strengths and limitations. ML-based methods include interpretable and uninterpretable approaches, with interpretable methods aiming to define analytical expressions for CLs, while uninterpretable methods rely on neural networks and other black-box techniques. Model-free methods integrate material observations directly into the solution process of solid mechanics problems. The review also discusses the distinction between supervised and unsupervised methods, emphasizing the importance of data availability and the role of physics constraints in improving model reliability. It covers various ML techniques, including symbolic regression, sparse regression, neural networks, support vector regression, and Bayesian inference, highlighting their applications in constitutive modeling. The article also addresses the challenges of data scarcity and the need for efficient data sampling strategies, such as grid-based, uniform, and Latin hypercube sampling. The review concludes with an overview of earlier reviews in the field, emphasizing the importance of data-driven approaches in material design and the integration of experimental and ML methods. It highlights the potential of deep reinforcement learning in optimizing experimental designs and the need for further research to improve the reliability and generalization of data-driven constitutive models. The article underscores the importance of combining data with physics to develop robust and accurate models for solid mechanics applications.This review article presents a comprehensive overview of data-driven (DD) techniques for discovering, encoding, surrogate, or emulating constitutive laws (CLs) that describe the path-independent and path-dependent response of solids. The objective is to provide a structured taxonomy of methodologies developed over the past decades, discussing the benefits and drawbacks of various techniques for interpreting and forecasting mechanics behavior across different scales. The article distinguishes between machine learning (ML)-based and model-free methods, categorizing approaches based on their interpretability and learning process, while addressing key challenges such as generalization and trustworthiness. It also discusses data sampling techniques, design of experiments, verification, and validation. The article begins by explaining the fundamental equations in solid mechanics, including conservation principles, kinematics, and constitutive laws. It highlights the traditional empirical nature of material modeling and the shift from limited to large-data regimes due to advances in experimental and computational methods. The review then classifies DD approaches into ML-based and model-free methods, discussing their strengths and limitations. ML-based methods include interpretable and uninterpretable approaches, with interpretable methods aiming to define analytical expressions for CLs, while uninterpretable methods rely on neural networks and other black-box techniques. Model-free methods integrate material observations directly into the solution process of solid mechanics problems. The review also discusses the distinction between supervised and unsupervised methods, emphasizing the importance of data availability and the role of physics constraints in improving model reliability. It covers various ML techniques, including symbolic regression, sparse regression, neural networks, support vector regression, and Bayesian inference, highlighting their applications in constitutive modeling. The article also addresses the challenges of data scarcity and the need for efficient data sampling strategies, such as grid-based, uniform, and Latin hypercube sampling. The review concludes with an overview of earlier reviews in the field, emphasizing the importance of data-driven approaches in material design and the integration of experimental and ML methods. It highlights the potential of deep reinforcement learning in optimizing experimental designs and the need for further research to improve the reliability and generalization of data-driven constitutive models. The article underscores the importance of combining data with physics to develop robust and accurate models for solid mechanics applications.