- Strong modification of turbulent transport in fluid flows with chemical reactions or heterogeneous phase transitions (e.g., evaporation of droplets) is analyzed. It is shown that turbulent diffusion may be strongly depleted in chemically reacting flows or in flows with phase transitions. In addition, the existence of nondiffusive heat and mass fluxes of the components in the systems with chemical reactions or heterogeneous phase transitions is demonstrated. These fluxes can be interpreted as ``turbulent'' analogues of the known cross-effects in irreversible thermodynamics. The mechanism of ``turbulent'' cross-effects is completely different and is associated with turbulent transport in reacting flows. The analyzed effects may result in the excitation of a large-scale instability which causes formation of large-scale inhomogeneities in the spatial distributions of temperatures and number densities of admixtures. The obtained results are relevant to the atmospheric physics and turbulent combustion.