A generalized approach to the use of pulsed-gradient spin echo (PGSE) NMR methods for the measurement of flow and diffusion in porous media is presented, in which the fluid dynamics is probed over well-defined temporal and spatial domains. Various NMR techniques based on PGSE encoding are described in the context of standard theories of dispersion, with reference to Eulerian and Lagrangian coordinate frames. This away of methods provides access nor only to the dispersion coefficient and the mean local velocity but also to propagators relevant to spatial and temporal correlations. Methods investigated include flow imaging, average propagator analysis, dispersion measurement, velocity exchange spectroscopy, and flow diffraction based on scattering analysis. We apply these to a study of flow and dispersion of water in a packed bed of 90.7-mu m-dia. polystyrene latex spheres. Our measurements of the dependence on Peclet number of dispersion (parallel and perpendicular to the mean flow direction) are in excellent agreement with results reported in the literature. The scattering approach used here has potential for studying complex flow properties involving the interplay between hydrodynamic and structural characteristics of porous media.