There are several answers to the question "what we can do with it", such as 1) reprocess it and use it again; 2) keep it in the power plant pools or similar storage facilities; 3) dump it to some deserted place where it isn't a big problem (high depth, stable earth crust). In the past, UK just dumped nuclear waste in barrels into the sea, which seems kind of convenient and irresponsible, but if done right (better isolation from sea creatures), this could work too.
It is true that there is no single universally agreed upon answer. But that is the same as with all other waste. Most of waste gets either burned or dumped at some place. The same will happen to nuclear "waste", until people start reprocessing it.