So far as I know, the UK is still storing most of its waste in ponds. Says the inevitable Wiki quote:

Radioactive waste - Wikipedia, the free encyclopedia

In the United States alone, the Department of Energy states there are "millions of gallons of radioactive waste" as well as "thousands of tons of spent nuclear fuel and material" and also "huge quantities of contaminated soil and water."^[1] Despite copious quantities of waste, the DOE has stated a goal of cleaning all presently contaminated sites successfully by 2025.^[1] The Fernald, Ohio site for example had "31 million pounds of uranium product", "2.5 billion pounds of waste", "2.75 million cubic yards of contaminated soil and debris", and a "223 acre portion of the underlying Great Miami Aquifer had uranium levels above drinking standards."^[1] The United States has at least 108 sites designated as areas that are contaminated and unusable, sometimes many thousands of acres.^[1][2] DOE wishes to clean or mitigate many or all by 2025, however the task can be difficult and it acknowledges that some may never be completely remediated. In just one of these 108 larger designations, Oak Ridge National Laboratory, there were for example at least "167 known contaminant release sites" in one of the three subdivisions of the 37,000-acre (150 km²) site.^[1] Some of the U.S. sites were smaller in nature, however, cleanup issues were simpler to address, and DOE has successfully completed cleanup, or at least closure, of several sites.^[1]

Admittedly these are pounds, not tons, but it's still a lot of trash to take out and bury.

As I've said before, the most telling argument against nuclear is political - you simply can't trust governments and market-run economies to build nukes sensibly with a mature safety culture, or to clean up after themselves.

The fact that this may be possible in Sweden doesn't necessarily mean the problem has been solved elsewhere.