The Shakri were supposed myths in Time Lord history, said to be "the pest controllers of the universe".
The Shakri were led by "the Tally", though the Eleventh Doctor was unsure what the Tally was. It drove them to eliminate species that the Shakri considered pests. Seven was a significant number for the Shakri, as they always travelled in groups of seven and their cubes counted down from seven. (TV: The Power of Three)
During their planned genocide of humanity, the Shakri relied on cubes, both for reconnaissance and attack. They were small black cubes, indestructible by human means. When activated, they had a wide variety of functions, from reconfiguration, mood-changing or just playing music. They were then changed to stop human hearts.
The Shakri also used seven ships in another dimension to coordinate the attack. These ships were connected via wormholes to seven locations on Earth, which they monitored with droids disguised as humans. They also had minions which looked human except for their grill mouths. (TV: The Power of Three)
The Doctor explained that the Time Lords were taught about the Shakri when they were young, but believed them to be legends. (TV: The Power of Three) Romana knew of them as "characters in a nursery rhyme". (AUDIO: Babblesphere) They existed at all moments in time and space.
In the early 21st century, the Shakri decided that humans needed to be destroyed before they could colonise space. They sent millions of inert Shakri cubes to Earth, then did nothing with them. After a year, humanity had gotten used to them and taken them into their lives. At this point, they were activated for 47 minutes, learning all they could about humanity. After counting down from seven, they then stopped the hearts of anyone close by. The Shakri planned to release a second wave of cubes to kill the remaining humans, but the Eleventh Doctor was able to reverse the effects so that the cubes instead restarted the victims' hearts. (TV: The Power of Three)