Three different flow and transport phenomena considered here are hydrodynamic dispersion in heterogeneous porous media and aquifers, transport of passive particles in an oscillating flow field, and miscible displacement processes in heterogeneous reservoirs. At microscales all three phenomena are described by the classical convective-diffusion equation (CDE). The presence of long-range correlations at macroscales gives rise to a rich variety of phenomena that cannot be predicted by analyzing the CDE by classical methods. In particular, a new percolation model with long-range correlations provides a rational explanation for the hitherto unexplained field-scale experimental data for hydrodynamic dispersion in porous media and aquifers. Moreover, for transport in oscillating flow in convection cells percolation provides a novel relation between the dispersion coefficient and the Péclet number that cannot be predicted by other methods.