The critical state concept is a central theory of many constitutive models. However, it is modelled in different ways by different models and not always in a straightforward manner. The critical state can be defined by two dilatancy conditions, which allow understanding how constitutive models achieve the critical state. Moreover, it permits understanding some of their limitations. For instance, the Cam-Clay models are not well-suited for dense, or overconsolidated, soils as they cannot distinguish the phase transition point from the critical state. Consequently, they model the peak strength as a yielding point, which is in contraction with the stress-dilatancy theory. This paper explains in a simple manner how the critical state is achieved in three different models - Cam-Clay with and without sub-loading surfaces, and Nor-Sand - and illustrates these models highlighting some of their limitations.