Humans have successfully landed on a moving comet in space. The landing, which was executed by the European Space Agency on November 12, 2014, is illustrated in this video (which was released prior to the successful completion of the mission).

The European Space Agency explains the plan as such:

"Rosetta will release its Philae lander when approximately 22 kilometres from the centre of the comet. A signal confirming the separation will arrive at ground stations on Earth 28 minutes and 20 seconds later while the lander’s descent to the surface will take seven hours. On the way down, Philae will take a series of images and onboard instruments will sample the dust, gas and plasma close to the comet’s surface and measure any magnetic field.

Philae’s three lander legs will absorb the momentum of impact and use it to drive an ice screw in each foot into the surface. At the same time two harpoons will fire to lock the probe onto the surface and a small thruster on top will counteract the impulse. Once anchored to the nucleus, Philae will begin its primary science mission, based on its initial battery lifetime of 64 hours."

As to be expected when dealing with moving objects over 500 million kilometres from Earth, everything didn't go perfectly according to plan. The Philae lander wasn't able to take advantage of its solar panels because it happened to land in a spot where the sun couldn't reach it, and so it currently out of power.