A limited overview is given of the theoretical understanding of edge plasmas in fusion devices. This plasma occupies the thin region between the hot core plasma and material walls in magnetic confinement devices. The region is typically formed by a change in magnetic topology from close magnetic field lines (i.e. the core region) and open field lines that contact material surfaces (i.e. the scrape-off layer (SOL)), with the most common example being magnetically diverted tokamaks. The physics of this region is determined by the complex interaction of plasma with neutral species in the presence of plasma turbulence, and impurity radiation is often an important component. Recent advances in modelling strong, intermittent micro-turbulent edge-plasma transport are given, as is the closely coupled self-consistent evolution of the edge-plasma profiles in tokamaks. In addition, selected new results are given for the characterization of edge-plasmas behaviour in the areas of edge-pedestal relaxation and SOL transport via edge-localized modes, impurity formation including dust and magnetic field-line stochasticity at the edge of tokamaks.