A NMR study of the structure-dynamics relationships in heterogeneous materials is presented. In the first part, transport in soft-matter systems is studied using the pulsed field gradient NMR technique (PFG NMR). The molecular crowding effect in biological matter has been addressed using polymer solutions as model systems. By performing ensemble-based diffusion studies, the earlier obtained data on anomalous diffusion have been complemented. The transition to normal diffusion on a larger time scale has been shown. Taking advantages of the NMR approach, transport properties of microemulsions consisting of micellar colloids dissolved in liquid crystals have been investigated. The self-diffusivities measured under equilibrium conditions have shown weak correlations with microscopic ordering and macroscopic phase transitions occurring in the systems under study. The formation of micelles is shown to be decisive for macroscopic separation at the isotropic-nematic transition. The second part of the thesis covers heterogeneous effects in diffusion for fluids in porous solids, as probed using a combination of NMR diffusometry and structure characterization methods. Ionic liquids have been investigated, revealing a complex behavior under confinement. The attempts to correlate the observed characteristics of the ionic liquids with their internal chemical structure were undertaken. Finally, the series of nanoporous glasses with tunable pore structure characteristics were studied. Strong correlations between their structure and the preparation conditions as well as between the resulting transport properties have been shown.