Observations of tracer transport in fluids generally reveal highly complex patterns shaped by an intricate network of transport barriers. The elements of this network appear to be universal for small diffusivities, independent of the tracer and its initial distribution. In this talk, I will discuss a mathematical theory to predict diffusive transport barriers and enhancers solely from the flow velocity, without reliance on expensive diffusive or stochastic simulations. This theory yields a simplified computational scheme for diffusive transport problems, such as the estimation of salinity redistribution for climate studies and the forecasting of oil spill spreads on the ocean surface. I will illustrate the results on observational ocean velocity data.