<p>Physics-Informed Neural Networks are neural networks which combine data-driven deep learning and physical models by incorporating physical laws into their loss function. They are promising and flexible solvers or surrogates for problems governed by partial differential equations, including forward and inverse cases, and during the last few years they have been applied to a variety of problems in physics and engineering. In this survey, we present a comprehensive analysis of PINNs while focusing on their applications in materials science. We examine their foundational form and components, expand on enhancing strategies, and explore various aspects of their practical implementations. For materials modeling, problem cases are systematically organized based on the main scope of publications found in the literature. For this survey, problems are categorized into heat transfer related problems, including multiphysics cases, materials properties and design, materials durability, stress analysis, as well as problems related to porous media and multi-phase materials. Finally, we discuss the current challenges and limitations of PINNs, their advantages, and potential future research directions.</p>