The onset of cavitation is strongly enhanced by the presence of rough surfaces or impurities in the liquid. Despite decades of research, the way the geometry of these defects promote the nucleation of bubbles and its effect on the kinetics of the process remains largely unclear. We present here a comprehensive explanation of the catalytic action that roughness elements exert on the nucleation process for both pure vapor cavities and gas ones. This approach highlights that nucleation may follow nontrivial paths connected with a sharp decrease of the free energy barriers as compared to flat surfaces. Furthermore, we demonstrate the existence of intermediate metastable states that break the nucleation process in multiple steps; these states correspond to what is commonly known as cavitation nuclei. A single dimensionless parameter, the nucleation number, is found to control this rich phenomenology. The devised theory allows one to quantify the effect of the geometry and hydrophobicity of surface asperities on nucleation. Within the same framework, it is possible to treat both vapor cavitation, which is relevant, e.g., for organic liquids, and gas-promoted cavitation, which is commonly encountered in water. The theory is shown to be valid from the nano- to the macroscale.