Cells have a blueprint to make proteins, but not to organize these and other molecules into organelles, cells, tissues, and organisms. For this, they largely rely on self-organization. However, we lack a mechanistic understanding of how cells self-assemble cytoskeletal structures and how these dynamically reorganize in animal cells and tissues to perform fundamental mechanical functions required to reshape, move or resist deformation. I will report our efforts to understand through mathematical and computational modeling the active self-organization of the actin and intermediate filament cytoskeleton within cells and its impact in tissue mechanics and self-organization. Time permitting, I will also discuss the self-organization of patterns of hydraulic cracks.