Fatty acids (FAs) are essential elements of all cells and have significant roles as energy substrates, components of cellular structure and signalling molecules. The storage of excess energy intake as fat in adipose tissue is an evolutionary advantage aimed at protecting against starvation, but in much of today's world, humans are faced with an unlimited availability of food, and the excessive accumulation of fat is now a major risk for human health, especially the development of type 2 diabetes (T2D). Since the first recognition of the association between fat accumulation, reduced insulin action and increased risk of T2D, several mechanisms have been proposed to link excess FA availability to reduced insulin action, with some of them being competing or contradictory. This review summarises the evidence for these mechanisms in the context of excess dietary FAs generating insulin resistance in muscle, the major tissue involved in insulin-stimulated disposal of blood glucose. It also outlines potential problems with models and measurements that may hinder as well as help improve our understanding of the links between FAs and insulin action.