Several different carbon-capture technologies have been proposed for use in the cement industry. This paper reviews their attributes, the progress that has been made toward their commercialization, and the major challenges facing their retrofitting to existing cement plants. A technology readiness level (TRL) scale for carbon capture in the cement industry is developed. For application at cement plants, partial oxy-fuel combustion, amine scrubbing, and calcium looping are the most developed (TRL 6 being the pilot system demonstrated in relevant environment), followed by direct capture (TRL 4-5 being the component and system validation at lab-scale in a relevant environment) and full oxy-fuel combustion (TRL 4 being the component and system validation at lab-scale in a lab environment). Our review suggests that advancing to TRL 7 (demonstration in plant environment) seems to be a challenge for the industry, representing a major step up from TRL 6. The important attributes that a cement plant must have to be "carbon-capture ready" for each capture technology selection is evaluated. Common requirements are space around the preheater and precalciner section, access to CO2 transport infrastructure, and a retrofittable preheater tower. Evidence from the electricity generation sector suggests that carbon capture readiness is not always cost-effective. The similar durations of cement-plant renovation and capture-plant construction suggests that synchronizing these two actions may save considerable time and money.