We present a new model for corrosion-induced cracking in reinforced concrete. Corrosion is a dominant degradation mechanism in 70-90 % of prematurely deteriorating reinforced concrete structures. Corrosion-induced cracking eventually results in spalling or delamination of concrete cover and thus significantly contributes to the degradation process. In order to accurately capture this complex chemo-mechanical phenomenon, the state-of-the-art knowledge of the underlying processes has been incorporated into three interconnected sub-models – (i) a reactive transport model for the transport and precipitation of ferrous, ferric and chloride ions in the concrete pore space, (ii) a precipitation eigenstrain model for the corrosion-induced pressure of precipitates (rust) accumulating in the concrete pore space, (iii) a phase-field fracture model calibrated to accurately describe the quasi-brittle fracture of concrete. In addition, a damage-dependent diffusivity tensor has been employed to capture the enhanced transport of ferrous and ferric ions away from the steel surface and chloride ions to the steel surface through corrosion-induced cracks. The proposed model has been numerically implemented using the finite element method. The ability of the model to accurately capture the evolution of surface crack width in time has been validated with experimental data. The modelling results have revealed that precipitates (rust) are found to be largely near the rebar but also spread up to millimetres away from the steel surface, reducing the precipitation-induced pressure and delaying cracking. Also, the fracture has been found to proceed even with the partial saturation of the concrete pore space with precipitates. A parametric study has identified the important role of the mechanical properties of rust, highlighting the need for appropriate characterisation studies. Spalling and delamination have been studied in two- and three-dimensional settings showing the dominant role of rebar spacing. In addition, the results reveal the important impact of the non-uniformity of chloride-induced corrosion on surface crack width.