Recent technological advancements open up possibilities of optimizing the functional behavior of structures in engineering applications by adding a stage of design at the material scale. For instance, additive manufacturing enables a superior control in the shaping and patterning of material constituents. This modern rationale poses the question of developing: 1) novel paradigms for material micro/nanostructure, 2) novel methods for the optimization of material topology, 3) novel manufacturing techniques. The combination of multiple and contrasting materials, with differences in elastic and inelastic responses, is a challenging strategy that could lead to new classes of smart behaviors. For instance, this approach is followed by Nature, where biological tissues are hierarchically optimized by means of chemo-biological mechanisms. Hence, the significance and the need of novel material design approaches has been highly increasing in recent years. Computer-assisted techniques allow to speed-up and reduce the costs of optimization procedures for material topology and constituents’ properties. The predictive capabilities of numerical simulations are highly affected by the accuracy and robustness of constitutive models and how effectively constitutive formulations are translated into computational environments. Therefore, the development of advanced computational approaches for the analysis and the modelling of material responses arises as an emergent and urgent topic. The workflow for the design of advanced materials is associated with major issues which involve several aspects at the cutting edge of Computational Mechanics. From the engineering point of view, the optimization of computer-assisted techniques is crucial and it is based on the delicate balance between accuracy, robustness and cost. To reach this goal, a solid understanding of methodological aspects and a wide knowledge of available approaches are essential. The aim of the course is to present theoretical fundamentals, the current state-of-the art, and future directions of “computational approaches for the analysis of the mechanics of materials” with the aim of “providing a modern perspective on in silico tools for the design of advanced materials”. The homogenization problem will be faced coupling multiscale and multiphysical analyses. Advanced computational approaches will be presented, highlighting advantages and disadvantages of traditional and novel techniques in different case studies. Materials for modern engineering demands will be focused, spanning from metamaterials, through smart hydrogels and magneto-mechanically coupled composites to MEMS. The described theoretical and methodological approaches will allow to discuss aspects of key importance through the entire material production process: starting at the design stage, through topology optimization, up to material manufacturing. The course will appeal to doctoral students and postdoctoral researchers from academia and industry with an interest in the constitutive modeling of multiphysical and/or multiscale response of materials, and with a background in engineering or in material sciences.