The Rhodians, also known as the Rhodia, were a humanoid species on Rhodia. They had a long history of combat and civil war with the other species on Rhodia, the Quill. (TV: Co-Owner of a Lonely Heart)
The one Rhodian known to have visited Earth, Charlie Smith, was outwardly indistinguishable from humans.
They possibly had a more alien appearance originally, although it is not clear whether that was their true form or simply one imagined by April MacLean when she pictured the fall of Rhodia. In that form, they had mottled, greyish skin tone, with dark patches framing the eyes. Their chin line was accentuated by blunt spines like a puffer fish. Their hair could be blue. (TV: For Tonight We Might Die)
The Rhodians were a cultured, learned society. (TV: For Tonight We Might Die) They were ruled by the King and Queen of Rhodia, as well as Charlie the Prince of Rhodia, heir to the throne. (TV: Co-Owner of a Lonely Heart)
The Rhodians had legend of the Cabinet of Souls, where the soul of every Rhodian was to go after dying. While Prince Charlie once thought it empty — just a nice bed time story for children to make death less scary — he later opened it, and found life inside.
They had what Miss Quill considered a cruel punishment, but Charlie considered just. This punishment was carried out after they defeated the Quill in battle. They released a creature into the brain called an arn. Once it dug itself in with its poisonous claws, the arn would telepathically link the host to a particular Rhodian, and force them to become their effective slave. If they were to break a rule, or fail to protect their master, the arn would kill them. (TV: For Tonight We Might Die)
Tanya Adeola questioned their morality. When Charlie asked her not to, she said as long as their morality continued to look like slavery, she would go on asking questions. (TV: Co-Owner of a Lonely Heart)
According to Miss Quill, the Rhodians ate up all the planet's resources, including that of the Quill. They tried to help the Quill, but in the process made them so dependent that they could never recover.
The two peoples were eventually at war with each other. The Rhodians won, and Miss Quill, the foremost of the Quill freedom fighters, was implanted with an arn that indentured her to Charlie. The Rhodians reasoned that the indenture of the Quill leader to the future Rhodian leader would facilitate peace.
While they were busy fighting amongst themselves, the Shadow Kin arrived, and killed everyone, Quill and Rhodian alike. Charlie managed to escape thanks to Miss Quill. The pair were subsequently rescued by the Twelfth Doctor, who brought them to Coal Hill Academy to start a new life. Charlie managed to bring the Cabinet of Souls with him, a device that contained the souls of all the fallen Rhodian. (TV: For Tonight We Might Die)