The goal of this project is to promote finite element modeling of 3D crack propagation by a phase field approach. One key objective is the advancement of a non-conventional discretisation technique with exponential shape functions. Together with an adaptive remeshing strategy, this aims at an efficient, accurate and robust implementation for phase field fracture simulations of crack growth, branching, kinking and coalescence. Further key objectives are several enhancements of existing phase field fracture models in order to make them applicable to more complex physical situations, including finite deformation settings and plastic material response. Another key objective is the incorporation of a physically sound crack closure criterion, including crack face contact and friction. With this feature, the phase field model will be applicable to sliding cracks under compression, as they appear frequently in geological setups and concrete structures. The influence of crack face contact is also of interest for the prediction of fatigue crack growth. Especially in geometrically complex fatigue crack scenarios, the capability of the phase field model to account for crack kinking and branching is very advantageous. Thus, a further topic is the development of a novel fatigue crack evolution law based on the enhanced phase field fracture model.