The consideration of fundamental physical laws when performing machine learning predictions within the fields of materials mechanics and processing of large-scale complex systems, can reduce errors and enhance generalization. While physics-based models contain assumptions and simplifications; thus, produce errors, data-driven models can demand relatively large data sets to represent fundamental relationships. These respective disadvantages can be compensated for via a synergistic combination of both modelling methods. A particular hybrid modeling approach is given by a physics-based model (either analytical or numerical) that is data-mined and corrected via a data-driven discrepancy model to reach the desired reference solution, in this work stemming from either experimental measurements or high-fidelity simulations. The prediction targets span from process behavior and process temperature to resulting material properties of complex processes. A number of different application examples are presented for a variety of materials processing techniques, such as Laser-Shock-Peening, a technique used for the modification of residual stresses in metallic materials; Friction Surfacing, a solid-state processing technique of metallic materials used for additive manufacturing; as well as Hot Rolling, whereby metal strips with specific geometries and mechanical properties are produced. Additionally, physics-based feature engineering via dimensionless formulations of inputs and outputs based on a dimensionality analysis according to the Buckingham Pi theorem enables the reduction of prediction scatter and allows for physical extrapolation. Generally, it is shown that the integration of physics into the data science workflow can enhance prediction performance and generalization, particularly with scarce data and to the extent of physical extrapolation.