During his final battle against the Red Skull, Captain America was forced to kill his old foe. In doing so, he gained possession of the Cosmic Cube. Knowing that he might be tempted to use the Cosmic Cube, he turned it over to the one person who would not use it no matter what and would also refuse to give it to Cap, no matter how badly he asked for it: the Black Panther. The Panther sealed the Cube in a special container in his shrine of the Panther God, where it would remain untouched for years.
During the time that humanity was being unknowingly mutated by the Terrigen Mist released into the air by the Black Bolt, wildlife all over the world became endangered as humans began to consume more meat. Facing extinction of various species on a global scale, the Black Panther converted Wakanda into a wildlife preserve. At this time, the animals in the Wakanda wildlife preserve began to mutate as well into humanoid animal forms. For the longest time, everyone believed that this was caused by the Terrigen Mist. When Black Panther was asked to lend his resources in finding a cure for the global mutation, he refused to do so because it would silence what he believed was the animal gods finally being given voice. The highly spiritual Panther would consult the Ani-Men for guidance.
However, once the true nature of humanities global mutation (caused by Celestial manipulation centuries ago and exposure to the Terrigen Mist) and other animals being found on Earth that weren't mutated (sea life appeared unaffected, and Mar-Vell spotted a lone dove that was unmutated as well) led to the conclusion that the Terrigen Mists were not responsible for the Ani-Men's mutation.
When Mar-Vell came to Wakanda (now under siege by an army of Wendigo) to collect the Cosmic Cube, Mar-Vell revealed to the king of Wakanda that it was his subconscious desire to have the animals be able to speak to him was the cause. He explained that the Cosmic Cube didn't need to be touched in order to be used, and that his desires activated it. He further explained that the Ani-Men were created in his own image, and their words were essentially him talking to himself. This revelation shook Black Panther and the Ani-Men to their core.
Later, when the Wendigo were able to break through their barriers, Black Panther determined that it was time for the kingdom of Wakanda to relocate to a better location. With the help of the X-Men and Banner & Hulk, they moved the entire kingdom along with the Ani-Men to the Savage Land. With the help of the Ani-Men (who were goaded into helping in the fight by the X-Men's Dogface, who might be a member of the Ani-Men) they killed off the Wendigo army, which was revealed to be Jamie Madrox.
The Ani-Men were last seen in a new habitat establishment in the Savage Land, where they have lived in peace for the time being, although their peace was temporarily disturbed when the Savage Land was attacked by Belasco and an army of Dire Wraiths. This attack was foiled by Mar-Vell and his followers.