This review concerns the application of disperse dyes to poly(ethylene terephthalate) fibres using aqueous immersion dyeing processes and the roles of both elevated dyeing temperatures and carriers in such dyeing systems. This part of the paper presents a review of the fundamental properties and characteristics of poly(ethylene terephthalate) fibres, disperse dyes and dyeing accelerants. In the next part of the paper, the various theories and concepts which have been proposed to explain the promotional effects imparted by elevated dyeing temperatures and carriers to disperse dye uptake on PET and other types of fibre, are reviewed and analysed, from the viewpoints of the essential physico‐chemical aspects of both the aqueous disperse dye/PET and disperse dye/carrier/PET systems. The final part of the paper will present a dual‐mode mechanistic model of the disperse dye adsorption process which can be used to account for the promotional effects imparted by both elevated dyeing temperatures and dyeing accelerants on disperse dye uptake.This article is protected by copyright. All rights reserved.