Because of the various time-altering storylines in the DC universe, there have been several incarnations of the Brainiac. He is a super-powerful android who takes the form of a green, bald alien from the planet Colu.

Brainiac was the one who shrank the Kryptonian city of Kandor.


DC ANIMATED

Brainiac a computer on the planet Krypton who knew about the end of Krypton but didn't say anything so he could save himself so that he could be the
only Kryptonian left. Brainiac was designed on Krypton and is a Krypton computer system. He decided to let the people die so that he could be saved. He felt as if he was the one who should be saved because he holds Krypton's information. Brainiac was suspected of knowing about the destruction by Jor-el, Superman's father. He knew about the end of the Planet but Brainiac covered it up to make it seem as if the earthquakes on Krypton was nothing. Brainiac was discovered by Jor-el downloading himself and was chased by the police before the planet ended. Before the planet exploded, Brainiac finished downloading himself. Clark's archenemy is Brainiac because of this reason. Brainiac came to Earth and attacked Superman, who he knew was Jor-el's son from Krypton. Brainiac made copies of itself.

In the Justice League episode Brainiac made a copy of himslef near New Genesis. He took control of a base near Apokolips and activated it. He was taken over by Darkseid, but Orion and the Justice League destroyed both Darkseid and Brainiac. In Divided We Fall it seems that Luthor was held captive by Brainiac but Brainiac and shot a beam at Luthor but the beam happened to be a copy of Brainiac himself. It began to control Luthor's actions. Luthor planned on inplanting his brain into a new Amazo body created by Cadmus. Amanda Waller and the Justice League destroyed the Amazo. Flash used the power of the Speed Force to create light speed vibrations and destroyed Brainiac. Brainiac seems to be alive, since Luthor has him still in his head. After experiencing all the power Brainiac had given him, Luthor decided to find Brainiac so he can feel his former glory which was taken from him by the Flash

Reboot?

When a "Brainiac" arrived on Earth searching for Kryptonians, Superman defeated it and brought it to the Fortress of Solitude.  He mentions to Supergirl that Brainiac is an alien from the planet Colu and he has an extremely powerful telekinetic mind.  The first time he encountered him, Brainiac possessed the mind of Milton Fine.  Each time Brainiac has arrived, it's been through a different body, sometimes organic, sometimes robotic. 

Supergirl quickly tells him that the one they are looking at is just a probe like the others.  She tells him that he's never actually met Brainiac and that no one has.  The thought of Brainiac actually frightens Supergirl.  Months before she left Krypton, Brainiac invaded.  Hundreds of robotic probes were sent into the city of Kandor.  People were killed and a barrier was placed surrounding the city.  Then Kandor vanished.