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We review and discuss some different techniques for describing local dispersion properties in fluids. A recent Lagrangian diagnostics based on the finite scale Lyapunov exponent (FSLE), is presented and compared to the finite time Lyapunov exponent (FTLE), to the Okubo–Weiss (OW) and Hua–Klein (HK) criteria. We show that the OW and HK are the limiting case of the FTLE, and that the FSLE is the most efficient method for detecting the presence of cross-stream barriers. We illustrate our findings by considering two examples of geophysical interest: a kinematic model of a meandering jet, and Lagrangian tracers advected by stratospheric circulation.