This work presents results of studies of transport of molecules and ions in several selected types of nanostructured materials. For the most part, the transport studies were performed using an experimental technique, which is known as pulsed field gradient nuclear magnetic resonance (PFG NMR). The systems under study can be divided into two types: (i) organized soft matter systems, such as ionic liquids and, (ii) porous solids, such as zeolites and mesoporous silicas. All studied systems exhibit well-defined structure on the length scales ranging from one nanometer to several hundreds of nanometers. Study of transport properties over a wide range of length scales, which were in many cases comparable with the sizes of structural inhomogeneities (particles, domains, etc.) of the investigated systems, allowed clarifying structural properties of these systems as well as provided new information on the relationship between these properties and diffusion of molecules and ions in these systems.

Pulsed field gradient NMR allows performing measurements of the mean square displacements (MSD) of molecules and ions as a function of diffusion time. This work presents development and implementation of this technique under conditions of high magnetic field (17.6 T) and ultra high gradient strengths (30 Tm^-1) with precise temperature control over a temperature range from 218.2K to 423K. Application of ultra high gradients resulted in a possibility of diffusion measurements on the length scale of displacements as small as 90 nanometers under the conditions of high signal-to-noise ratios resulting from a high magnetic field. In addition to PFG NMR, also another NMR technique was used, viz. continuous flow hyperpolarized ¹²⁹Xe 2D exchange spectroscopy (CFHP ¹²⁹Xe 2D EXSY). This technique works on the principle of NMR tracer exchange and allows for monitoring time dependence of uptake or release of NMR labeled molecules in regions or domains of interest. This technique was used in “the work in progress” section reported later in the thesis. Simplistic Dynamic Monte Carlo simulations were also performed to complement experimental Xe 2D EXSY studies.