The Year of the Slow Invasion was a gradual invasion of Earth over a twelve month period in the first half of the 21st century by the Shakri cubes so that the Shakri could eliminate humanity.
History
Believing humanity to be a plague that would bring ruin to the universe should they go out into the stars to colonise, the Shakri decided to conduct "pest control" by sending their cubes to infiltrate 21st century Earth in the month of July. They were inactive, but still were believed to be a threat; the Eleventh Doctor, Kate Stewart, and Brian Williams decided to watch the cubes until some kind of activity occurred, though the Doctor eventually got bored and didn't resume observing the cubes until he returned to Earth in June. The cubes were subjected to numerous tests by UNIT to see what could destroy them; through human methods, it was impossible. Eventually, the Shakri began using an android to command fake orderlies, which kidnapped multiple humans over the course of the year.
The following July, every last cube performed some random function; some of them were harmful (such as spewing fire and causing mood swings) and some were just plain annoying (like playing the "Chicken Dance"). The cubes then sucked in electricity, using it to stop the hearts of one third of the human population. The Doctor infiltrated the Shakri ship and used the cubes' programming to restart the hearts they previously stopped. The contradiction of the Shakri's methods caused one of their ships to explode, sealing them back outside the universe. (TV: The Power of Three)