In the first incarnation of Brainiac, he was an green skinned android from the robot-dominated world of Colu-One who sought to collect information throughout the cosmos, coming into conflict with Superman over his diabolic capture of Krypton-One's city of Kandor with his shrinking ray. His brain patterns were borrowed from a dying scientist of that world to mimic humanity. After attempted to steal cities from Earth-One including its Metropolis, Brainiac came into conflict with Superman who became his greatest foe. Over the years, Brainiac would team up with other villains such as Lex Luthor and even become a member of the Anti-Justice League battling Superman's Justice League on multiple occasions. He would expand his mental might beyond his twelfth level intelligence, gaining abilities such as his force fields and brain blasts, and even expand his reach to battle other members of Superman's Family including Supergirl.
Wishing to make his new home in the Earth-Two universe, the Commander had like his counterpart faced the Man of Steel in battle. While on Earth-One, Superman was joined by the Justice League and Teen Titans in averting an invasion, here it fell upon the native Justice Society with the visiting Justice League and the Champion family assisting them. In both instances, Brainiac and Commander found a worthy implacable enemy in the Last Son of Krypton, who led the fight to topple these intergalactic egomaniacs from their insatiable thirst for conquest. In Brainiac's case, it was through Superman's manipulations of the sun to cause power spikes in the robotic rogue's cerebral cortex which cause him to lose his memory and plotting capabilities. Seeking refuge in hyperspace, the villain to humanity would next appear in the void between universes, having created a floating replica of Metropolis complete with a horde of Supermen robots that lured the Legion and the original Kryptonian Crusader into a trap. A trap they managed to circumvent, causing Brainiac to once more escape only to return during the Crisis on Infinite Earths to lead a villain war against five Earths.
In the case of the Commander, it took the combined cognitive capabilities of the Champion children and their aunt coordinated by Doctor Fate to create a dimensional rift, one into which Superman and his JSA and JLA allies could thrust the tyrant. Seeking to return him to his own universe, the Commander forced himself to remain in Earth-Two's plane of existence, at the cost of his own essence dissolving into all of that universe's reality, while the League and Society (like the Legion and Superman above) were thrust through dimensions into the void between universes albeit briefly. Interestingly, just as around this time that Brain Wave perished while battling his old ally Ultra-Humanite in interdimensional limbo... the new Brainiac's cosmic twin the Commander left his native universe for that of Earth-Two's.
However in the 30th century the original Brainiac form had reappeared and was in this future timeline consumed by a star going nova yet undergoing quite a different transformation from that of Stargrave, turning into storehouse of tremendous cosmic energy. In this form, the now insane android was intent of locating his most hated adversary in the form of Superboy, himself a member of the Legion of Super-Heroes, and of the offspring of his wayward progeny in the form of Legionnaire Querl Dox aka Brainiac Five. On one occasion, his genocidal tendencies seemingly led to the death of Ultra Boy, who was later located in inter dimensional limbo. Stargrave himself, although among the most powerful of villains in that era, was finally and decisively beaten by Dox never more to reappear.
Another android on Earth-Two had assumed the physical presence of Brainiac while possessing the awesome energies of Stargrave yet with the mental might originating not from Brain Wave nor the Commander but from Doctor Anton Hastor. Hastor had hijacked on enclave of scientists determined to being an end to World War II by means of technology thought to be from the stars, and used it versus the All-Star Squadron. This evil entity was also defeated by its master's arch-foe the Hawkman alongside his fellow All-Stars, with the body scrapped in some government warehouse until this very day.