Despite the popularity of variational phase-field models for fracture in purely mechanical problems, their application to the modeling of fracture in multi-physics problems is much more challenging and less reported. This might be attributed, on the one hand, to the theoretical complexity involved in multi-physical phenomena, and on the other hand, to the cumbersome implementation of these coupled models in home-made platforms. In this work, the phase-field cohesive zone model (PF-CZM) is adopted as the prototype model to address fracture in various multi-physics problems, e.g., the thermo-mechanical fracture due to thermo shocks in ceramics, the hydrogen-assisted cracking in metals involving chemo-mechanical fracture, the shrinkage induced cracking due to chemo-thermo-mechanical coupling in early-age concrete, and the electro-mechanical fracture in piezoelectric ceramics, etc. The theoretical and numerical aspects are categorized into modular structures. A couple of representative benchmark examples are considered for the validation. Not only the qualitative crack patterns but also the quantitative global responses are compared against available experimental test data. It is found that the typical characteristics of fracture in the considered multi-physics problems can be well captured. Moreover, as in the purely mechanical counterpart, the predicted crack pattern and global responses are insensitive to the phase-field length scale, making the PF-CZM promising for modeling fracture in other more involved multi-physics problems.