Phase-field approaches to fracture are gaining popularity to compute a priori unknown crack paths. In this work the sensitivity of such phase-field approaches with respect to its model specific parameters, that is, the critical length of regular- ization, the degradation function and the mobility, is investigated. The susceptibility of the computed cracks to the setting of these parameters is studied for problems of linear and finite elasticity. Furthermore, the convergence properties of different solution strategies are analyzed. Monolithic and staggered solution schemes for the solution of the arising nonlinear discrete systems are studied in detail. To conclude, we demonstrate the versatility of the phase-field fracture approach in a real-world problem by comparing different simulations of conchoidal fracture using structured and unstructured meshes.