1. Introduction -- 2. Image extraction and virtual microstructure simulation -- 3. 2D- and 3D-mesh generation by Voronoi tessellation -- 4. Microstructure characterization and morphology-based domain partitioning -- 5. The Voronoi cell finite element method (VCFEM) for 2D elastic problems -- 6. 3D Voronoi cell finite element method for elastic problems -- 7. 2D Voronoi cell FEM for small deformation elastic-plastic problems -- 8. Voronoi cell FEM for heat conduction problems -- 9. Extended Voronoi cell FEM for multiple brittle crack propagation -- 10. VCFEM/X-VCFEM for debonding and matrix cracking in composites -- 11. VCFEM for inclusion cracking in elastic-plastic composites -- 12. Locally enhanced VCFEM (LE-VCFEM) for ductile failure -- 13. Multi-scale analysis of heterogeneous materials : hierarchical concurrent multi-level models -- 14. Level-0 continuum models from RVE-based micromechanical analysis -- 15. Adaptive hierarchical concurrent multi-level models for materials undergoing damage.