Background
Professor Eobard Thawne, also known as the Reverse-Flash, is a time-traveling criminal from the 22nd century, and the archenemy of The Flash.
Professor Eobard Thawne, born in 2151, was obsessed with The Flash. He spent years figuring out how he came to be, and after managing to duplicate the process that granted the speedster his powers, he successfully managed to gain a connection to the Speed Force. However, he subsequently discovered, through time travel, that he was destined to become The Flash's greatest enemy, and would never become him, causing Eobard to despise his former idol. Becoming the Scarlet Speedster's "reverse", Eobard would then make it his life's mission to take as much as he can from him, travelling through history in order to find the time period the Flash is from and learn his name.
War with The Flash, and Harrison Wells
After their first encounter in 2016, in which he suffered a severe beating at the hands of his nemesis, Eobard would fight the Flash for many years. One day, he learns his enemy's name, and travels back in time to kills him as a child, only for Barry, who had already experienced this from the perspective of a child, his 2015 and 2016 selves, as part of a predestination paradox, to follow him and save his younger self, leaving his mother at Eobard's mercy.
After killing Nora Allen, inadvertently resulting in him losing his powers and being stranded in the past, Thawne realized he needed the Flash's speed to go back to his own time. To that end, he orchestrated an elaborate plan involving the murder of Tess Morgan and impersonating scientist Harrison Wells after stealing the scientist's DNA with futuristic technology. Under the guise of Wells, Thawne started STAR Labs and sped up Wells' research by five years, all to further his own goal.
He kept a close watch on Barry, and deliberately let the particle accelerator at S.T.A.R. collapse to create the Flash. When Barry's powers emerged, "Wells" immediately positioned himself as mentor to assist in the development of his powers Despite regaining his abilities back and being numerous times faster than Barry, Eobard's connection to the Speed Force was unstable. He continued to train Barry in hopes that he will be fast enough to create a wormhole to allow him to return back to his time. Eobard was erased from existence when Eddie Thawne kills himself, causing a black hole to emerge from the wormhole.
Flashpoint
After Barry traveled back in time and prevented his mother's murder, Eobard was subsequently taken into the altered present time and made prisoner. He taunted his adversary about the consequences of tampering with the timeline, dubbing the new one "Flashpoint", and was proven correct as Barry's memories of the original timeline started to fade away. Ultimately deciding he needed to undo the change, Barry was forced to release Eobard and return him to the night of Nora's murder in order to allow him to execute it and set the timeline back to its prior version. After doing so, however, Eobard once again taunted Barry by stating everything would not be exactly the same as before the Flashpoint, and fled.
Legion of Doom
Eobard acquired knowledge of an event in his future and sought to change it by travelling throughout time to collect relics, and form partnerships with various individuals to further his own goals, such as Damien Darhk and Malcolm Merlyn.