They are basically facing 4 problems, ensuring long term cooling of the cores, ensure cooling of the spent fuel pools, prevent release of radioactive material and mitigate the consequences of the releases that will continue for a while. I want to speak a bit more about cooling in this blog post since it is the most crucial problem.
This is a blog by people very knowledgeable about nuclear power. It contains a somewhat day-to-day account of the events in Fukushima, as well as a lot of other info.
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