In light of the increasing demand for energy sources in the world and the need to meet climate goals set by countries, there is growing global interest in high temperature gas cooled reactors (HTGRs), especially as they are known to be inherently safe nuclear reactors. The safety of HTGRs results, among other, from the nature of the nuclear fuel used in them in the form of coated TRISO particles (tri-structural-isotropic) and the reduction of the total amount of radioactive waste generated. This paper reviews numerous methods used to ensure the sustainable, feasible management and long-term storage of HTGR nuclear waste for the protection of the environment and society. The types of waste generated in the HTGR cycle are presented as well as the methods of their characterization, which are important for long-time storage and final disposal. Two leading nuclear fuel cycle strategies, the once-through cycle (direct disposal or open cycle) and the twice-through cycle (recycling or partially closed cycle), are discussed also in relation to TRISO spent fuel. A short review of the possibilities of treatment of TRISO spent nuclear fuel from HTGR reactors is made.