Instead of shutting down for weeks to replace fuel rods, pebbles are placed in a bin from which spent pellets are removed from the bottom and new ones added to the top (actually, each pellet goes through the cycle several times).
The pebbles are the size of tennis balls, and it takes 150,000 of them in the inner core and 380,000 in the outer core (annulus) to fuel a reactor of 120 MW. Each pebble contains carbon and uranium, and is surrounded by hard silicon carbide. Even if the helium coolant were to leak away, it would take weeks before meltdown would even be a possibility.
A 15MW demonstration reactor was built in Germany in the 1960s. It ran successfully for 21 years, until the project was axed in the wake of the Chernobyl disaster.
[add more here, particularly about the pilot projects, opposition from the public, and political and economic aspects]
A prototype pebble bed reactor is proposed for Koeberg, South Africa.