AbstractAchieving 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. (© 2014 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)