This page contains information regarding Star Trek: Discovery, and thus may contain spoilers.
The Ba'ul were a spacefaring species native to the planet Kaminar. They were commonly thought to be the predator species that fed on the Kelpiens, a pre-warp sentient species also native to the planet. However, the Ba'ul were in fact originally the prey species, and post-vahar'ai Kelpiens their predators. (ST: "The Brightest Star"; DIS: "An Obol for Charon", "The Sound of Thunder")
The Ba'ul were aquatic, with a humanoid form. They had spindly limbs and digits, long tendrils on their heads, glowing red eyes, and protrusible spines along their backs. Their bodies were covered by a black, smoky, oily substance. (DIS: "The Sound of Thunder", "Su'Kal")
In the mid-1st century, predation by the Kelpiens drove the Ba'ul to the brink of extinction, with fewer than 260 individuals surviving. Using their technological superiority, the Ba'ul turned the tide and wiped out all the post-vahar'ai Kelpiens.
To ensure that they would never again be threatened, the Ba'ul forced the remaining Kelpiens into subservience and imposed upon them a belief system called the Great Balance, designed to prevent any Kelpien from evolving into their post-vahar'ai predatory form. Under this doctrine, the Kelpiens were led to believe that they were required to offer themselves for ritual sacrifice when they reached vahar'ai, so as to preserve Kaminar's ecosystem.
The Ba'ul developed warp drive in 2237. Two years later, the Federation starship USS Archimedes made first contact in response to a signal sent by Saru. The Ba'ul reacted with hostility and received Starfleet's assurance that they would not interfere with Ba'ul internal affairs.
In 2257, the USS Discovery was led to Kaminar by a red burst. The Ba'ul became aware that Saru had undergone vahar'ai and captured him and his sister Siranna, intending to neutralize them to preserve the Great Balance. Within their stronghold, Saru broke free of his restraints and commandeered Ba'ul technology to broadcast a signal, derived from the Sphere by the Discovery crew, that triggered vahar'ai across all the Kelpiens on the planet.
As they were on the verge of losing control of the Kelpiens, the Ba'ul activated their pylon network in an attempt to exterminate the entire Kelpien population. Before they could do so, the Red Angel arrived and disabled their technology with an immense electromagnetic pulse. In the aftermath, Saru and Siranna were resolute that the Kelpiens would find a way to coexist with the Ba'ul. (DIS: "The Sound of Thunder")
By the 31st century, the Ba'ul had formed an alliance with the Kelpiens and joined the Federation. The All-Seeing Eye of the Ba'ul had evolved to become a symbol of protection. Saru was gratified that the Ba'ul and the Kelpiens had managed to put aside their differences at last. (DIS: "Die Trying", "Su'Kal")
Society and culture
The Ba'ul were led by the Ba'ul High Council. They were isolationist in nature; they chose to interact with the Kelpiens solely via technology, such as that by the mid-23rd century no Kelpien had seen a Ba'ul in living memory.
The Ba'ul feared the Kelpiens, believing their predatory instincts to be uncontrollable. Thus, they saw the Great Balance as the only way to prevent the Kelpiens from destroying everything, and they were prepared to enact genocide on the Kelpiens rather than allow them to evolve past vahar'ai en masse.
By 2257, the Ba'ul were a warp-capable civilization with knowledge of transporters and force fields. They defended their homeworld with sentry ships and operated fighter craft. The Ba'ul maintained networked pylons in every Kelpien village, with which they could monitor the Kelpiens and summon those who had reached vahar'ai for harvesting by their ships; this led to the Kelpiens calling the Ba'ul the "Watchful Eye", which was said to rule the sky. When a Kelpien reached vahar'ai, they were expected to be honored that the Watchful Eye had chosen them to maintain the Great Balance. The pylons were controlled from a massive underwater stronghold. The Kelpiens were forbidden to keep any pieces of Ba'ul technology they found. (ST: "The Brightest Star"; DIS: "The Sound of Thunder", "Such Sweet Sorrow, Part 2")