How do you deal with nuclear waste?

High level waste which is the fission products from using fuel in a nuclear reactor, is contained in the spent fuel which is discharged into a water filled tank eventually. There it is kept for some time, probably several years, before being handled. The waste is retained in the fuel by the zircaloy cladding of the fuel rods, so it doesn't leak out, unless there is any deterioration in this cladding. In the US the fuel rods have simply been kept on the power station site. In some plants the tanks provided have been filled up and shielded flasks have had to be provided to hold some of the oldest and least active spent fuel. There is no further handling route at present, as I understand it the intended repository at Yucca Mountain Nevada is on hold.
In the UK and France in contrast fuel has been transported from the power plants to central treatment plants (Sellafield in the UK) where it has been chemically treated to recover useful material, the fission products are then stored and some have been treated to make vitrified material. However there is no long term repository yet, so this is being stored on the treatment sites.