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While the community has seen many advances in recent years to address the challenging problem of Fine-grained Visual Categorization (FGVC), progress seems to be slowing—new state-of-the-art methods often distinguish themselves by improving top-1 accuracy by mere tenths of a percent. However, across all of the now-standard FGVC datasets, there remain sizeable portions of the test data that none of the current state-of-the-art (SOTA) models can successfully predict. This paper provides a framework for identifying and studying the errors that current methods make across diverse fine-grained datasets. Three models of difficulty—Prediction Overlap, Prediction Rank and Pair-wise Class Confusion—are employed to highlight the most challenging sets of images and classes. Extensive experiments apply a range of standard and SOTA methods, evaluating them on multiple FGVC domains and datasets. Insights acquired from coupling these difficulty paradigms with the careful analysis of experimental results suggest crucial areas for future FGVC research, focusing critically on the set of elusive images that none of the current models can correctly classify. Code is available at catalys1.github.io/elusive-images-fgvc.