We do little to even try to contain that waste, and aren't even thinking of how to 'get rid of it'. The effects of this radioactive waste are totally overshadowed by the 'conventional' pollution caused by coal.
Nuclear power compares pretty well to this.
In addition to the reductions in air quality that kills vast number of people from coal - multiple Chernobyls every year - coal plants also pump vast quantities of radioactive material like uranium particles into the air.
While nuclear waste would pump nastier stuff into the air, we know the consequences from Chernobyl: Most of it gets washed out and end up on the ground quickly. What doesn't tend to be less dangerous particulates like cesium isotopes.
I'm obviously not suggesting that we should, but that pretty much the worst possible scenarios you can think of would still end up killing fewer people than coal.
But all things considered I have given up hope that that will actually work in time - thus, by all means, we should build as-safe-as-possible nuclear power plants for the transition and shut down all fossil-based versions immediately.
A long half-life means that the material is less radioactive. By definition.
Soon it will be possible to use most of the waste as fuel:
"...Fast reactors can "burn" long lasting nuclear transuranic waste (TRU) waste components (actinides: reactor-grade plutonium and minor actinides), turning liabilities into assets. Another major waste component, fission products (FP), would stabilize at a lower level of radioactivity than the original natural uranium ore it was attained from in two to four centuries, rather than tens of thousands of years"
http://en.wikipedia.org/wiki/Integral_fast_reactor
The worry people have about nuclear waste is greatly overblown. The amounts generated are small and in a relatively short amount of time we can use most of this "waste" to generate electricity.
As a comparison, how does coal waste compare to that?
"Coal ash – the waste material left after coal is burned – contains arsenic, mercury, lead, and over a dozen other heavy metals, many of them toxic."
http://www.psr.org/environment-and-health/code-black/coal-as...
"The study found that levels of radioactivity in the ash were up to five times higher than in normal soil," https://phys.org/news/2015-09-radioactive-contaminants-coal-...
How much coal waste is produced per year? Is it small enough to deal with easily?
"According to the American Coal Ash Association's Coal Combustion Product Production & Use Survey Report, nearly 130 million tons of coal ash was generated in 2014."
https://www.epa.gov/coalash/coal-ash-basics#03
Has any of the general public been killed though coal waste disasters? Lots of times:
http://www.catawbariverkeeper.org/issues/coal-ash-1/coal-ash...
NASA has estimated that using nuclear power has saved an estimated 1.8 million lives that would have been lost if the power has been replaced by fossil fuels: https://climate.nasa.gov/news/903/coal-and-gas-are-far-more-...
(And yes, I know the people who oppose nuclear power usually will say they don't like coal and natural gas either, but we are going to need a predictable, reliable form of base load power for a long time. One of these three ways of generating electricity has much fewer health consequences than the other.)