This review article highlights state-of-the-art data-driven techniques for discovering, encoding, surrogating, or emulating constitutive laws that describe the path-independent and path-dependent response of solids. The authors aim to provide an organized taxonomy of methodologies developed over the past decades and discuss the benefits and drawbacks of various techniques for interpreting and forecasting mechanics behavior across different scales. They distinguish between machine-learning-based and model-free methods, categorizing approaches based on their interpretability and learning process/type of required data, while addressing key problems of generalization and trustworthiness. The review also touches on relevant aspects such as data sampling techniques, design of experiments, verification, and validation. The primary goal is to offer a structured presentation of how data-driven techniques can advance constitutive modeling in solid mechanics, providing an overview of how these techniques can exploit large amounts of available observations to obtain richer constitutive laws that accurately predict material behavior. The paper is structured to cover earlier reviews, data sampling approaches, DD modeling for path-independent problems, and discussions on current limitations and conclusions.This review article highlights state-of-the-art data-driven techniques for discovering, encoding, surrogating, or emulating constitutive laws that describe the path-independent and path-dependent response of solids. The authors aim to provide an organized taxonomy of methodologies developed over the past decades and discuss the benefits and drawbacks of various techniques for interpreting and forecasting mechanics behavior across different scales. They distinguish between machine-learning-based and model-free methods, categorizing approaches based on their interpretability and learning process/type of required data, while addressing key problems of generalization and trustworthiness. The review also touches on relevant aspects such as data sampling techniques, design of experiments, verification, and validation. The primary goal is to offer a structured presentation of how data-driven techniques can advance constitutive modeling in solid mechanics, providing an overview of how these techniques can exploit large amounts of available observations to obtain richer constitutive laws that accurately predict material behavior. The paper is structured to cover earlier reviews, data sampling approaches, DD modeling for path-independent problems, and discussions on current limitations and conclusions.