The transport barrier which exists at the plasma edge in the high-confinement (H-mode) regime is now recognized as importantto global energyconfinement. Recently, detailed measurements of the width and height ofbarriers in electron and ion density and/or temperature have been made onseveral divertor tokamaks. These results are reviewed, with an emphasis onscalings of the pedestal height and width. Many experiments observesituations in which the limiting pedestal pressure gradient is well describedby ideal ballooning stability. In some cases the extreme edge is in the`second stable' regime. Differences between the widths Δ of pedestalsinelectron and ion temperature and densities are noted in several experiments. Some reported scalings are ΔTi = 3.3(ε)1/2ρi,pol on JT-60U, and ΔPe/R∝βpol,ped0.4 on DIII-D. ΔTe isindependentof plasma current in many experiments. Theoretical modelling of the fullydeveloped H-mode pedestal is reviewed. Several recent predictions of thepedestal parameters and their scalings are outlined and compared with experiments.