The course will review the fundamental computational approaches for materials modeling in the framework of a hierarchical multi-scale paradigm: first-principles methods, classical and reactive molecular dynamics, coarse-grained methods and continuum methods. The basic theory at the base of each approach will be outlined with a quick summary of the main (open-source) codes available for each described computational method. By reviewing the latest advances in the scientific literature, it will be shown how multi-scale computational modeling is gaining a pivotal role in the field of computational materials science and how it is used to understand and design new structures and new materials following a “bottom-up” approach from atomistic to real-world scale resolution. In the perspective of applying multi-scale modeling to the investigation and design of materials for technological applications with peculiar response properties, the attention of the course will be put on basic structure/property relationships applied to a variety of both inorganic (nano-composite) and bio-based materials.