The most long-lived radioactive wastes, including spent nuclear fuel, must be contained and isolated from humans and the environment for a very long time. Disposal of these wastes in engineered facilities, or repositories, located deep underground in suitable geologic formations is seen as the reference solution.[1] The International Panel on Fissile Materials has said:


Common elements of repositories include the radioactive waste, the containers enclosing the waste, other engineered barriers or seals around the containers, the tunnels housing the containers, and the geologic makeup of the surrounding area.[3]

The ability of natural geologic barriers to isolate radioactive waste is demonstrated by the natural nuclear fission reactors at Oklo, Africa. During their long reaction period about 5.4 tonnes of fission products as well as 1.5 tonnes of plutonium together with other transuranic elements were generated in the uranium ore body. This plutonium and the other transuranics remained immobile until the present day, a span of almost 2 billion years.[4] This is quite remarkable in view of the fact that ground water had ready access to the deposits and they were not in a chemically inert form, such as glass.

Despite a long-standing agreement among many experts that geological disposal can be safe, technologically feasible and environmentally sound, a large part of the general public in many countries remains skeptical.[5] One of the challenges facing the supporters of these efforts is to demonstrate confidently that a repository will contain wastes for so long that any releases that might take place in the future will pose no significant health or environmental risk.

Nuclear reprocessing does not eliminate the need for a repository, but reduces the volume, reduces the long term radiation hazard, and long term heat dissipation capacity needed.

/... http://en.wikipedia.org/wiki/Deep_geological_repository

In 1982, Congress passed the Nuclear Waste Policy Act directing the Department of Energy to build and operate a repository for used nuclear fuel and other high-level radioactive waste. The act set a deadline of 1998 for the Energy Department to begin moving used fuel from nuclear energy facilities.

To fund the federal program, the act established a Nuclear Waste Fund. Since 1983, electricity consumers have paid into the fund one-tenth of a cent for every kilowatt-hour of electricity produced at nuclear power plants. These fees continue to accumulate at a rate of $750 million a year, and the fund accrues more than $1 billion in interest each year. The fund’s balance, as of May 2013, is more than $29 billion. Without a high-level radioactive waste management program and annual congressional appropriations, these funds are not available for their intended purpose.

In 1987, Congress amended the Nuclear Waste Policy Act, directing the Energy Department to exclusively study Nevada’s Yucca Mountain, a remote desert location, as the site for a potential repository for geologic disposal of used nuclear fuel. After two decades of site studies, the federal government filed a construction license application in 2008 for a repository at Yucca Mountain.

However, President Obama in 2010 stopped the Yucca Mountain license review and empaneled a study commission to recommend a new policy for the long-term management of used fuel and high-level radioactive waste. In January 2012, the Blue Ribbon Commission on America's Nuclear Future published its final recommendations, most of which are supported by the industry. The Energy Department’s used fuel management strategy to implement the commission’s recommendations was issued in January 2013.

/... http://www.nei.org/Issues-Policy/Nuclear-Waste-Management/Disposal

The Strategy for the Management and Disposal of Used Nuclear Fuel and High-Level Radioactive Waste is a framework for moving toward a sustainable program to deploy an integrated system capable of transporting, storing, and disposing of used nuclear fuel and high-level radioactive waste from civilian nuclear power generation, defense, national security and other activities.

The Strategy addresses several important needs. First, it serves as a statement of Administration policy regarding the importance of addressing the disposition of used nuclear fuel and high-level radioactive waste; it lays out the overall design of a system to address that issue; and it outlines the reforms needed to implement such a system. Second, it presents the Administration’s response to the final report and recommendations made by the Blue Ribbon Commission on America’s Nuclear Future (“BRC”). It also responds to direction in the Joint Explanatory Statement accompanying the Consolidated Appropriations Act, 2012, to develop a strategy for the management of used nuclear fuel and nuclear waste in response to the BRC’s recommendations. Third, this strategy represents an initial basis for discussions among the Administration, Congress and other stakeholders on a sustainable path forward for disposal of nuclear waste.

/ and blah blah blah... http://energy.gov/sites/prod/files/Strategy%20for%20the%20Management%20and%20Disposal%20of%20Used%20Nuclear%20Fuel%20and%20High%20Level%20Radioactive%20Waste.pdf
(18-page .pdf) The essence of the Obama Plan? Back to the drawing-board on square one, basically. And lots of political opportunities...

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