The theory of extracting coherent vortex properties from individual Lagrangian trajectories is reviewed and is shown to exhibit excellent performance when applied to an idealized numerical model of an unstable nonlinear eddy on a beta-plane. The method is then applied to a set of 3310 surface drifter trajectories from the Gulf of Mexico. In addition to the anticyclonic Loop Current Eddies, two types of energetic cyclonic variability are observed. The first is associated with a persistent feature in the southern Gulf of Mexico, termed the Campeche Gyre. The second is small-scale, high-Rossby number events---with V/(fR) between 0.15 and 0.35---that are conjectured to originate in the intense cyclonic shear zone of the inflowing Loop Current, and that are observed in both the eastern and western portions of the basin. Strong anticyclonic activity in the northwest corner of the Gulf, seen in some numerical models, is not observed in the data. Comparison with several realistic numerical models serves to (i) further examine the method’s ability to accurately recover eddy structures and (ii) assess the models’ performance at reproducing the observed eddy fields. Implications for eddy lifecycles, transport, and mixing are discussed.