Abstract: Lagrangian Coherent Structures (LCS) are the time varying generalization of separatrices (invariant manifolds), which divide the space of a dynamical system into trajectories that have different dynamical behaviors. For example, in a jellyfish, which fluid particles will get entrained into the jellyfish and which will be used for propulsion? Similarly, what fluid parcels will get entrained into a hurricane and which will get detrained? How does melting polar ice affect the thermohaline circulation? LCS answers these and other questions related to mixing and transport through the use of recently developed theoretical and computational methods in dynamical systems.