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 quasiperiodic microstructure using heuristic computational approaches or asymptotic techniques and multiscale modeling of materials with disordered microstructure based on computational and variational homogenization methods.