For more than thirty years, considerable efforts have been carried out in order to evaluate the possibility of disposing off high level wastes in deep geological formations. Different rock types have been examined, such as water-undersaturated tuffs (USA), granitic rocks (Canada, Sweden, Finland), clays (France, Belgium, Switzerland), rocksalt (Germany). Deep clays and granites, (provided that the most fractured zones are avoided in the second case) are considered to fulfill most allocated functions, either on short term (reversibility) and long term. Chemically reducing conditions favor the immobilization of actinides and most fission products by precipitation, coprecipitation and sorption. If oxididizing conditions prevail, the safety demonstration would mostly rely on the performance of artificial confinement systems. Rocksalt offers limited performance considering the issue of reversibility, which is now perceived as essential, mostly for ethical and sociological reasons. For more than twenty years, the importance of geochemistry has been continuously increasing to define boundary conditions for major processes such as metal corrosion, waste package dissolution, radionuclide speciation and migration. Orders of magnitude in terms of solubility, corrosion rate have be gained in chemically reducing systems. This input of geochemistry is probably the reason why clayey host rocks have received more and more attention. The long term behavior of waste packages has also been studied in more details, and less conservative estimates of their durability are now available. Major pending questions, concerning for instance the role played by radiolysis in the dissolution of the spent fuel matrix have been now clarified. It is now well established that in most systems in which reducing conditions dominate, the major release at the outlet will come from the most soluble fission products (129I, 36Cl) , and moreover far below recommended annual dose rates. In such systems, actinides remain stuck in the near field. However, several issues would deserve additional research programs, and as a first priority, a clear description of time/space succession of processes during the evolution of the repository. This will allow a better representation of coupled processes in PA, such as the influence of gases (H2) generated by corrosion on the long term dynamics of the resaturation. Geochemical interactions between the host formation and the engineered systems (packages + barriers) are still unsufficiently described. Additional gains in performance could be obtained when taking into account processes such as isotopic exchange. Imaginative solutions, employing ceramic- carbone composite materials could be proposed to replace heavy and gas-generating overpacks, or to accomodate the small but probably significant amount of " ultimate " wastes, that will be inevitably produced by Generation IV reactor systems.