This paper focuses on the highly radioactive, long-lasting nuclear waste produced by the currently operating fission reactors and on the way to deal with the sensitive issue of spent fuel reprocessing. The review includes a short description of the fission process and a detailed analysis of the more hazardous radioisotopes produced either by secondary reactions occurring in the nuclear installations or by decay of the fission fragments. Also outlined are the strategies presently adopted to minimize the harmfulness of the nuclear waste to be disposed and discussed advanced options and possible solutions proposed for the recycling of the used fuel and for the reusing of some technologicaly relevant radioisotopes.