The pursuit of accurate models of multiscale and multiphysics systems is a pacing item in computational physics. This talk focuses on novel ideas for the development of coarse-grained models through the use of statistical mechanics-inspired and data-informed techniques. The first part of the talk focuses on a modeling framework that combines the Mori-Zwanzig formalism with the Variational Multiscale method. It is shown that unresolved numerical effects in multiscale systems lead to a non-local residual-based memory term. This memory term is used as a starting point for model development and displays commonalities with techniques such as adjoint stabilization, artificial viscosity, and upwinding. The second part of the talk focuses on integrating data into the model development process. A data-informed modeling methodology will be discussed. This approach extracts discrepancies using inverse modeling and converts them into functional forms using machine learning. The approach is shown to be capable of addressing model form inadequacies.