This article is devoted to high level waste management. A synthesis of the high level waste (HLW) typology and key characteristics is given, showing that nuclear glass and spent nuclear fuel need to be considered for long term disposal, depending on national strategies. A rationale for selecting a relevant conditioning process is then presented, describing the parameters and constraints to take into account. A brief description of the vitrification processes, the sole industrially deployed conditioning process for HLW, is then presented. The vitrified waste interim storage strategy is described. The knowledge about the long term performance of HLW, spent nuclear fuel and nuclear glass, in geological disposal is then detailed. Finally, the development of alternative conditioning processes for HLW are briefly presented.