The reaction of slaked lime with atmospheric CO2 in the presence of humidity leads to the formation of cementing carbonate phases in traditional aerial lime mortars and plasters. This carbonation reaction also affects the setting and degradation of hydraulic lime mortars and modern cement. Here, we present an overview of the existing knowledge on carbonation of lime-based binders, which are experiencing a revival as compatible material for the conservation of the built heritage and new sustainable construction. First, the carbonation reaction is defined and its importance in a range of technical and natural processes is outlined. This sets the ground for presenting a review of existing mechanistic models for the carbonation of lime-based materials, including the recent interface-coupled dissolution-precipitation model, and the understanding of carbonation in terms of non-classical crystallization theory. Kinetics models and experimental results for carbonation of lime-based binders (crystals and powder, as well as mortars/plasters) and its acceleration are presented and discussed. Finally, conclusions and future research directions are indicated.