Recent progress in the experimental and theoretical studies of Edge Localised Modes (ELMs) physics is reviewed for the reactor relevant plasma regimes, namely the high confinement: H-modes and Advanced Scenarios. Theoretical approaches to ELM physics from a linear ideal MHD stability analysis up to non-linear transport models with ELMs are discussed with respect to the experimental observations, in particular the fast collapse of pedestal pressure profiles, magnetic measurements and SOL transport during ELMs. The key parameters that are presently identified to reduce the energy losses in Type I ELMs are operation at high density, high edge magnetic shear and high triangularity. High confinement H-mode scenarios at high triangularity and high density with small ELMs (Type II), mixed regimes (Type II and Type I) and combined Advanced regimes at high bp are discussed for present tokamaks. The optimum combination of high confinement and small MHD activity at the edge in Type II ELMs scenarios is of interest to ITER. However, to date, these regimes have been achieved in a rather narrow operational window and far from ITER parameters in terms of collisionality, edge safety factor and bp. The compatibility of the alternative Internal Transport Barrier (ITB) scenario with edge pedestal formation and ELMs is also addressed. Edge physics issues related to the possible combination of small benign ELMs (Type III, Type II ELMs, Quiescent Double Barrier) and high performance ITBs are discussed for present experiments (JET, JT-60U, DIII-D) with respect to their relevance for ITER. Successful plasma edge control at high triangularity (~0.5) and high density (~0.7nGR) in ITB scenarios in JET is reported. Active control of ELMs by edge current, pellet injection, impurities and external magnetic perturbations creating an ergodic zone localized at the separatrix are discussed for present experiments and their perspective in a future reactors.