Stratified shear flows, where the `background' velocity and density distribution vary over some characteristic length scales, are ubiquitous in the atmosphere and the ocean. At sufficiently high Reynolds number, such flows are commonly believed to play a key role in the transition to and maintenance of turbulence, and hence to be central to irreversible mixing of the density field. Parameterizations of such irreversible mixing within larger scale models of the ocean in particular is a major area of uncertainty, not least because there is a wide range of highly scattered and apparently inconsistent experimental and observational data. In this talk I consider two idealized flows, one continuously forced and one freely-evolving. Both flows clearly exhibit emergent critical behaviour. This behaviour suggests that consideration of criticality is a fruitful approach for the resolution of the apparent inconsistencies in data, as well as for the construction of robust and useful parameterisations of irreversible mixing by sheared, stratified turbulence.