A critical and long-standing need within the petroleum industry is the specification of suitable petrophysical properties for mathematical simulation of fluid flow in petroleum reservoirs (i.e., reservoir characterization). The development of accurate reservoir characterizations is extremely challenging. Property variations may be described on many scales, and the information available from measurements reflect different scales. In fact, experiments on laboratory core samples, well-log data, well-test data, and reservoir-production data all represent information potentially valuable to reservoir characterization, yet they all reflect information about spatial variations of properties at different scales. Nuclear magnetic resonance (NMR) spectroscopy and imaging (MRI) provide enormous potential for developing new descriptions and understandings of heterogeneous media. NMR has the rare capability to probe permeable media non-invasively, with spatial resolution, and it provides unique information about molecular motions and interactions that are sensitive to morphology. NMR well-logging provides the best opportunity ever to resolve permeability distributions within petroleum reservoirs. We develop MRI methods to determine, for the first time, spatially resolved distributions of porosity and permeability within permeable media samples that approach the intrinsic scale: the finest resolution of these macroscopic properties possible. To our knowledge, this is the first time that the permeability is actually resolved at a scale smaller than the sample. In order to do this, we have developed a robust method to determine of relaxation distributions from NMR experiments and a novel implementation and analysis of MRI experiments to determine the amount of fluid corresponding to imaging regions, which are in turn used to determine porosity and saturation distributions. We have developed a novel MRI experiment to determine velocity distributions within flowing experiments, and developed methodology using that data to determine spatially resolved permeability distributions. We investigate the use of intrinsic properties for developing improved correlations for predicting permeability from NMR well-logging data and for obtaining more accurate estimates of multiphase flow properties--the relative permeability and capillary pressure--from displacement experiments. We demonstrate the use of MRI measurements of saturation and relaxation for prediction wetting-phase relative permeability for unstable experiments. Finally, we developed an improved method for determining surface relaxivity with NMR experiments, which can provide better descriptions of permeable media microstructures and improved correlations for permeability predictions.