Achieving high pedestal pressures in H(high)-mode plasmas confined in tokamaks is critical for obtaining fusion burning plasmas in ITER. Recent characterizations of quasi-equilibrium plasma parameter profiles in low collisionality H-mode pedestals in the DIII-D tokamak are briefly summarized. Critical plasma transport properties (large radial electron heat flow, density pinch) that establish the transport barrier structure of the pedestal profiles are identified. The paleoclassical transport model, which naturally includes a density pinch, is shown to provide the minimum electron heat and density transport in the pedestal. Microinstabilities can provide additional plasma transport within and especially at the top of pedestals. Macroscopic peeling-ballooning (P-B) instabilities cause periodic edge localized modes (ELMs) that limit the temporal and spatial growth of the pedestal initially and between ELMs. Externally imposed 3D resonant magnetic perturbations (RMPs) in the pedestal have been used to stabilize P-B modes and suppress ELMs. A magnetic flutter model of plasma transport induced by the 3D RMPs has been developed for low collisionality DIII-D pedestals. Comparisons of it with data on ELM suppression by RMPs indicate it can provide a "diffusivity hill" at the pedestal top that can impede pedestal growth and thereby stabilize P-B modes and suppress ELMs. Finally, transport equations for plasma density, electron and ion pressures and, most importantly, the plasma toroidal rotation frequency (and hence, via radial force balance, the radial electric field) in the presence of plasma transport due to collisional, paleoclassical, microturbulence-induced and 3D field effects are presented. . These instabilities cause roughly periodic edge-localized-modes (ELMs) that abruptly relax the large edge plasma gradients and deposit undesirable bursts of plasma heat and particles on divertor plates. Pedestals evolve in various stages after an ELM [3]. Within a few to 10 ms after an ELM crash the pedestal quasi-equilibrium is re-established. But then it continues to grow slowly (for 10s of ms or longer) until a P-B instability precipitates an ELM. Externally imposed three-dimensional (3D) resonant magnetic perturbations (RMPs) have been used in DIII-D [4] to limit this progression and mitigate [5][6][7] or suppress [8] ELMs in tokamaks. The present challenge for edge plasma modeling is to develop and experimentally validate predictive transport models for the profiles and evolution of the pedestal density, temperature, flow and radial electric field profiles with and without 3D fields. This paper mainly reviews recent research results [9]-[16] on key paleoclassical and 3D transport processes involved in determining the structure of plasma profiles in low collisionality H-mode pedestals without [9] and with [8] RMPs in ITER-similar-shape DIII-D plasmas. The emphasis is on a validation process comparing theoretical models to relevant experimental data.This paper is organized as follows. The next section provides a characteriz...