For years, agencies like NASA and the European Space Agency have been studying NEOs, or near-Earth objects: asteroids, comets, and other space debris in close proximity to Earth. Now, an EU-funded project called NEOShield wants to investigate how to knock them off course with rockets, bombs, or gravitational pull. Launched last week, NEOShield aims to investigate the best way to protect Earth from a potential NEO collision and develop a plan to implement it. After a study period of three and a half years, NEOShield will likely propose a mission to test the technology it's settled on.
The vast majority of NEOs are nothing to worry about — they're either small enough that they burn up before impact or are on a trajectory that misses Earth altogether. However, an estimated 19,500 NEOs between 100 and 1,000 meters in size are largely uncharted and could cause serious damage if they were to hit. These impacts only happen about once every 2,000 years, but even an asteroid only 10 meters wide can release as much energy as an atomic bomb on hitting Earth.
In order to prevent larger impacts, NEOShield is working on better tracking these objects, and is researching the most widely-discussed deflection methods, particularly two that have already been looked into by major space agencies. The first, a "gravity tractor," would send a spacecraft to hover near the asteroid and pull it off course. The second is a "kinetic impactor," which would fire a large projectile to nudge the asteroid on a path away from Earth. A paper outlining the basic approaches — yes, including nuking the asteroid — is available here (PDF). You can also check out NASA's own NEO program, which has been charting the objects since 1998.