Abstract Process models and parameter estimation have long been fundamental tools in domains such as manufacturing, robotics, power plants, and biotechnology. Early modeling approaches relied on complex systems of mathematical differential and algebraic equations, known as science-based models, to capture process knowledge and scientific expertise. These models leverage physical and chemical properties, static and dynamic behaviors, and causal relationships among observed quantities to support predictive control and operational optimization. As white-box models, they provide transparency by uncovering the inner logic and decision-making steps of the process. However, the advent of Industry 4.0 has brought a surge in available data from industrial processes, driving the rapid growth of machine learning (ML) models. Those models excel at discovering patterns and nonlinear relationships in data, but often they are black-box models, i.e., they lack interpretability. To combine the strengths of science-based and ML models, hybrid models have emerged as a powerful solution. By integrating the transparency and domain knowledge of science-based approaches with the adaptability and predictive capabilities of ML, hybrid models enhance accuracy, robustness, and scalability. This chapter explores the foundations of hybrid models, their development, and applications, providing a comprehensive perspective on their transformative potential across various scientific and engineering domains. This work is done in the context of the AI-DAPT EU project.