I've read a recent popular mechanics article about mini nuclear reactors. From the comments on the article, many people are still terrified about how we process nuclear waste.
Let me first say that I worked for some time with EG & G Rocky Flats, in Rocky Flats, Colorado, on a research project that was directly involved with the development of processes to treat nuclear waste.
While I am not a chemist involved in radioactive chemistry, I developed models to predict chemical and mechanical processing times, in order to assess the overall requirements necessary to treat the many thousands of drums of nuclear contaminated waste that was sitting ABOVE ground.
In my view, the process of vitrification to research the process of "vitrification", which is essentially the process of embedding the radioactive ash into glass. The ash is created by oxidizing the radioactive waste in a slow, but controlled fashion. The resulting ash is mixed with molten glass. The ash incorporates itself into the glass matrix. After it solidifies, the radioactive components are embedded within the crystalline structure. This is much like how lead crystal is safe to drink from, even though it contains lead. The lead does not leach out of the glass. The following research paper from Pacific Northwest National Labs shows that unblanketed nuclear ash-containing glass has a nearly leachless rate for thousands of years.
The vitrified glass is still radioactive, and does heat up, but in a very predetermined way. The heat-up is determined by the relative amounts of ash and glass.
Finally, the vitrified radioactive glass can be "blanketed" That is, encapsulated by non-radioactive glass. This would reduce the leach rate by many orders of magnitude... That is to TENS to HUNDREDS of thousands of years.
Add to the fact that the vitrified waste can be stored in an underground salt dome, and basically there is no problem for humanity.