Modeling of deterioration of heat transfer (DHT) observed in fluid flows at supercritical pressure remains a challenge due to incomplete understanding of the underlying physics. Given the challenges involved in the experimental and computational study of this phenomenon, it is crucial that the growing collective experimental and computational data be periodically analyzed in a comparative manner through critical reviews. This paper aims to provide such a critical review. The experimental and computational evidence continues to support the postulate that streamwise acceleration of the lower density, near-wall fluid layer relative to the higher density bulk flow promotes reduced turbulent mixing and hence reduced convective heat transport. At lower mass flowrates, this may be driven by buoyancy force, whereas at higher thermal loading, the dominant driver may be the increased favorable streamwise pressure gradient prompted by the bulk flow acceleration. A discussion of these physical mechanisms and an assessment of related semi-empirical models constitute the scope of this review.