The two-parameter critical power (CP) model is a robust mathematical interpretation of the power-duration relationship, with CP being the rate associated with the maximal aerobic steady state, and W' the fixed amount of tolerable work above CP available without any recovery. The aim of this narrative review is to describe the CP concept and the methodologies used to assess it, and to summarize the research applying it to intermittent cycle training techniques. CP and W' are traditionally assessed using a number of constant work rate cycling tests spread over several days. Alternatively, both the 3-min all-out and ramp all-out protocols provide valid measurements of CP and W' from a single test, thereby enhancing their suitability to athletes and likely reducing errors associated with the assumptions of the CP model. As CP represents the physiological landmark that is the boundary between heavy and severe intensity domains, it presents several advantages over the de facto arbitrarily defined functional threshold power as the basis for cycle training prescription at intensities up to CP. For intensities above CP, precise prescription is not possible based solely on aerobic measures; however, the addition of the W' parameter does facilitate the prescription of individualized training intensities and durations within the severe intensity domain. Modelling of W' reconstitution extends this application, although more research is needed to identify the individual parameters that govern W' reconstitution rates and their kinetics.