We present here a continuous-discontinuous model for fracture based on the combination of two main ingredients: an adaptive phase-field model for diffuse cracks and XFEM enrichment for sharp cracks. Our adaptive phase-field model is based on considering only two types of elements in a fixed background mesh: h-refined elements along cracks, where a higher spatial resolution is needed, and standard elements in the rest of the domain. The strategy is specifically designed to avoid remeshing, transition elements or the handling of hanging nodes. Continuity of the displacement and damage fields in the non-conformal interface between adjacent elements of different type is imposed in weak form by means of Nitsche's method. This weak imposition of continuity leads to a very local refinement in a simple way: no tuning of Nitsche's parameter is required. This adaptive phase-field approach is then combined with XFEM enrichment. The phase-field equations are solved only in small subdomains around crack tips to determine propagation. With computational cost in mind, an XFEM discretization is used behind the tips to represent sharp cracks; this enables derefinement of the refined elements. Crack-tip subdomains move as cracks propagate in a fully automatic process. The continuity of the displacement field in the interface between the phase-field refined subdomains and the XFEM region is again imposed in weak form via Nitsche's method. In this continuous-discontinuous approach, the phase-field model plays the role of a crack tracking criterion that handles in a natural manner crack branching and merging. The robustness of the approach is illustrated by several examples, including branching and merging of multiple cracks in 2D, and twisting cracks in 3D.