Mesoscale eddies play an important role in transporting water properties, enhancing air-sea interactions, and promoting large-scale mixing of the ocean. They are generally referred to as “coherent” structures because they are organized, rotating fluid elements that propagate within the ocean and have long lifetimes (months or even years). Eddies have been sampled by sparse in-situ vertical profiles, but because in-situ ocean observations are limited, they have been characterized primarily from satellite observations, numerical simulations, or relatively idealized geophysical fluid dynamics methods. However, each of these approaches has its limitations. Many questions about the general structure and “coherence” of ocean eddies remain unanswered. In this study, we investigate the properties of 7 mesoscale eddies sampled with relative accuracy during 4 different field experiments in the Atlantic. Our results suggest that the Ertel Potential Vorticity (EPV) is a suitable parameter to isolate and characterize the eddy cores and their boundaries. The latter appear as regions of finite horizontal extent, characterized by a local extremum of the vertical and horizontal components of the EPV. These are found to be closely related to the presence of a different water mass in the core (relative to the background) and the steepening of the isopycnals due to eddy occurrence and dynamics. Based on these results, we propose a new criterion for defining eddies. We test our approach using a theoretical framework and explore the possible magnitude of this new criterion, including its upper bound.