Abstract.  We report on developments in the theory and computation of gyrokinetic turbulence in the tokamak edge. A new formulation of the gyrokinetic Lagrangian for the strong E×B-flow regime is been found, with clear correspondence to previous forms and to reduced MHD. Conservation of energy, momentum, entropy, and particles is demonstrated at both theoretical and computational level. Neoclassical phenomena and MHD equilibration are shown in our electromagnetic total-f phase-space computational model FEFI. Delta-f gyrokinetic edge turbulence is computed on the full flux surface with the local fluxtube model delta-FEFI and results on the edge/core transition are given. We also present ongoing gyrofluid studies of ELM crash scenarios, including the influence of the bootstrap current in an edge pedestal model on both the initial instability and the resulting turbulence. These studies and findings are centrally relevant to further understanding of the H-mode and pressure profile pedestal in large tokamaks.