The course covers the fundamentals on modelling heterogeneous materials with periodic, quasi-periodic or non-ordered microstructures. Metamaterials, auxetic materials, chiral and anti-chiral microstructures belong to this class and their design and optimization requires a deep knowledge of their mechanical behaviour. Topics addressed in the course concern the evaluation of the bounds to the effective elastic properties of heterogeneous materials, local (Cauchy continuum) and non-local (micromorphic and multipolar continuum) homogenization methods of materials with periodic and quasi-periodic microstructure using heuristic computational approaches or asymptotic techniques and multiscale modeling of materials with disordered microstructure based on computational and variational homogenization methods.