Abstract-The Modified Winding Function Theory (MWFTh), regarded as a very powerful and general theory, has been extensively used for the last 15 years. This paper performs an in-depth review of the mathematical and physical framework on which the MWFTh is based, showing that it is indeed very well suited to analyse machines with small air gaps of arbitrary shape. However, contrary to what is usually stated in the literature, it is also proved that its general formulae fail when applied to large air gaps. This major finding is deduced from two different approaches, both of which are later reinforced by numerical examples. In spite of that, there is an important industrial field (diagnosis techniques of salient-pole synchronous machines eccentricities) in which good theoretical results have been reported by applying the MWFTh to these large air-gap machines. This issue is addressed and clarified in the paper.