Different methods of removing radioactive compounds

We used a lot of time in researching and read a lot of scientific reports about how to remove radioactive compounds from waste water from nuclear reactors but mainly about how to do it with drinking water which is our focus. The main problems in general are that they are quite expensive or special skills are needed to be able to control the process because the waste it creates is even more radioactive than the water because it is concentrated. Usually they put the waste in landfills. But the waste will first disappear when the radioactive compounds has decayed to a stabile point which takes many, many years. It was a bit hard to understand the scientific language because it is not made for regular people to understand but made as scientific correct as possible.
What are the methods used to remove radioactive compounds from drinking water:
Most used: Absorption/filtration and through precipitation.
When working when removing radioactive compounds from water there are two main ways to do it:
Either put a reactant that will react with the radioactive compound and from a solid that will lay on the bottom on the water reserve.
Or put a absorbent agent that will absorb the radioactive compounds from the water.
The first method: Is said to be more complicated because you have to remove/scrape the solid of the bottom while with the other method it is easier to remove the absorbent.
In both cases it is hard and problematic to remove all the radioactive compounds and it is often expensive but even a little difference is better than no when we are talking radioactive contamination.
The contamination of the Japanese water comes from the meltdown of the nuclear reactors where the water that are supposed to cool the reactor down gets contaminated – and has a very high and dangerous radiation. The contaminated water is hard to control because contact with it is dangerous, eg, Beta radiation can go through the skin. And cause damage to the new skin cells that are produced.
One of the newest news is that Japan will dump some of the contaminated water in the ocean. http://www.scientificamerican.com/article.cfm?id=wrapup-4-japan-to-pump-radioactive
http://edition.cnn.com/2011/WORLD/asiapcf/03/24/japan.nuclear.workers/index.html?eref=edition_world&utm_campaign=Feed%3A+rss%2Fedition_world+%28RSS%3A+World%29