While the emergence of coherent structures in two-dimensional turbulence is 
well known, their description has primarily been Eulerian. In this talk we 
introduce a new, Lagrangian approach to coherent structures. We discuss an 
analytic result, a Lagrangian version of the Okubo-Weiss criterion, that enables 
one to extract coherent structure boundaries with great precision from 
experimental/numerical data. This criterion is Galilean invariant and hence 
eliminates the use of instantaneous stagnation points or other frame-dependent 
Eulerian features from the analysis of velocity data. We show applications to 
baropropic turbulence simulations. Finally, we discuss three-dimensional 
extensions and their applications.