The internationally recognised technical solution for high-activity waste is deep geological disposal. Finland and other countries have developed advanced programmes; the slower issue is often site selection, public acceptance, and governance. It is therefore not correct to say that 'nobody knows what to do'; it is correct to say that building disposal facilities requires long timescales, credible institutions, and consensus.
All FAQ
22.
Does nobody really know where to put nuclear waste?
False on a technical level; true that it is difficult on a political-social level.