Current Nuclear Power plants require the the use of the rare Uranium isotope U-235 and consequently only use one fifth of the total energy content. Next generation reactors forecast to be available in 2020's will use all the energy in Uranium or the more abundant Thorium. Nuclear reactors produce vast amounts of radioactive waste including large amounts of very long lived radioactive atoms. These radioactive particles are a product of the splitting of the atom. We are constantly exposed to low-level radioactivity from cosmic rays from outer space and naturally occurring radioactive isotopes which in general do not cause any harm.
However at high levels of exposure there are numerous biological effects of radiation. These cause cell death, cancer induction and can cause genetic damage. The waste of nuclear reactors is highly radioactive and long lived, and as a consequence must be isolated from humans for around 100,000 years. The current consensus is that Nuclear Waste should be disposed in secure containers and placed deep underground. Future technology promises to turn the long lived radioactive particles into shorter lived atoms.