Recent results on the understanding and scaling of several of the operational boundaries found in ELMy H-mode plasmas are presented. Divertor geometry is found to be important in determining the H-mode transition power and temperature. Recent experiments from different tokamaks find apparently conflicting evidence for the role of the edge neutral density in controlling the H-mode transition and further intermachine comparisons are clearly warranted. Significant progress has been made both on the understanding and on avoiding the H-mode density limit. Models based on divertor detachment and on MARFE physics reproduce the empirical density limit scalings. The density limit in ELMy H-modes has been increased by changing the profile of the density in the divertor and in the main plasma. Highly radiating ELMy H-modes are currently being studied and display some of the favourable characteristics of the TEXTOR radiated improved confinement (RI) mode.