Recycled aggregate concrete (RAC) includes recycled concrete aggregates (coarse and/or fine) as substitutes for natural aggregates as an approach to achieving a circular economy. Some concerns remain about its performance, including the carbonation resistance. The higher porosity of recycled concrete aggregates is logically a disadvantage, but the analysis must address many other factors. This paper provides an in-depth examination of recent advances in the carbonation performance of RAC. The emphasis is on factors that influence CO2 diffusion and the carbonation rate, e.g., the replacement ratio, source concrete quality, interfacial transition zone features, residual portlandite content, and porosity. The influences of previous treatments, combined action with supplementary cementitious materials, and loading conditions are also discussed. The replacement ratio has a significant impact on the carbonation performance of concrete, but it is also dependent on other factors. During carbonation, the physical effects of the porosity of the aggregate and the physical–chemical effects of the portlandite content in the adhered mortar are particularly important. The residual portlandite is especially significant because it is the primary hydration product responsible for the alkaline reserve for carbonation and the potential pozzolanic reaction, which are per se competing factors that determine the carbonation rate.