Phase-field models have shown great promise and flexibility for quantitative analysis of fracture. In this talk, I show our recent results where we extended these models to fracture of anisotropic materials and fatigue crack growth. By combining experiments using a biomimetic composite and phase-field modeling, in the first part of the talk, I show how one needs to take account of the process-zone size (and T-stress) to interpret the different kinking behavior in different sample geometries. In the second part of the talk, I show how the celebrated Paris power law emerges from a simple model based on the degradation of materials at the crack tip.