For decades, the atmosphere of Earth-One was a breeding ground of transmitted electronic waves produced from a myriad of computing equipment. Through this, the artificial consciousness known as the Construct was spawned, seeking to assert itself upon humanity and dominate it. To this end, it created robot automatons known as cannons which it sent to dispatch the one true viable threat to its rule...the Justice League of America. However, that team was able to defeat the synthetic being and attempted to erase it from existence.
Instead, it remained and reintegrated into Construct-II and Construct-III, seeking to mentally control Wonder Woman and the Injustice Gang separately and turn them against the League, then later using a reconstructed android known as Red Tornado. Each time, it failed in its objective to vanquish humanity.
In fact, a separate, distinct yet similar electronic entity was formed on the Red Tornado's home world of Earth-Two. This being had initially been the creation of Rex "Hourman" Tyler, who built his Crime-Caster artificial intelligence to predict any pending problems across the globe. In the future, this computer developed into a predictive machine which the sinister scientist known as T.O. Morrow plucked from the future of Earth-Two which he first witnessed through a temporal viewer on his native planet of Earth-One.
This Crime-Caster in the far future would further develop in certain timelines into the being known as the Hourman android, a self-described "intelligent machine colony". While Morrow brought a copy of this computer back to Earth-One following his defeat at the hands of the Justice Society and Justice League, Rex's first model and what it developed into remained on Earth-Two. And it seems that Morrow's copy of the Tyler machine was the core of the Construct as it formed following its creators defeat. On a fourth occasion, the Construct tried and nearly succeeded in subjecting humanity, however it's own creation in Red Tornado ultimately destroyed this creature completely.