In the ShowEdit
The Cybermen first appeared in 1966's The Tenth Planet. The Cybermen didn't give too much history, only that they were once humans from Earth's twin planet, Mondas, and that they were forced into turning most of their bodies into metal and plastic in order to survive. They also had to wipe away all emotion in order to keep themselves from going insane or dying. In the episode, they try to invade Earth and destroy it, as Mondas was absorbing too much energy from it, which would in turn, destroy their planet. However, the Doctor managed to stop the threat, with help from an Antartic base.
However, in later episodes, it is revealed that they managed to invade other planets such as Telos, home planet of the Cryons. The Cybermen were also involved in Cyber Wars, which caused the near extinction of them. These Cybermen were also affected by gold, which would choke their respiratory systems.
In the continuation series's episode Rise of the Cybermen/Age of Steel, another version of the Cybermen appear, this time from another universe. These Cybermen were created by John Lumic, a scientist who wanted to create a new life to take over after the human race. However, Lumic was attacked by one of his employees, seriously wounding him, forcing his creations to convert him into their Controller. To make sure they wouldn't end up as a big of a threat as the one from his universe, the Doctor fed the Cybermen emotions, which caused their systems to fight back and kill them. Lumic, who tried to stop the Doctor from escaping, died when he fell from a zeppelin into the exploding factory.
In the story Army of Ghosts/Doomsday, it is revealed that these Cybermen found a way into the Doctor's universe and tried to invade earth. However, they were quickly defeated when they came into contact and declared war on the Daleks. Any survivors were pulled into the Void by the Doctor, who was desperate to stop earth from falling into the hands of them or the Daleks. In 'The Next Doctor', it is revealed that, while in the Void, the two cybernetic races fought against each other and ultimately destroyed all life there. However, a small group escaped, arriving in Victorian London. Planning on creating a Cyberking, a giant Cyberman which required a human pilot, they planned to take over Earth and convert all humans into other Cybermen. However, the Doctor, with help from Jackson Lake, a man who thought he was the Doctor, and his 'companion' Rosita, the Doctor destroyed the Cyberking and sent the remains into the time vortex, where it was disintegrated.
It is also believed that both the Mondasian and Cybus Cybermen joined forces and forged their forces together, as in later episodes, the Cybus design is often used in the episodes. In 'Nightmare in Silver', the Doctor encounters a new variation of Cybermen, this time with the ability to adapt to new threats and convert any alien race into troops, including Time Lords. This variation later appears in 'The Time of the Doctor', helping other races fight the Doctor in the siege of Trenzalore, and team up with the Master to take over Earth in 'Dark Water/Death in Heaven'.
Like the Daleks, the Cybermen often return, stronger and smarter than the last time.
In the ModEdit
Cybermen attack the player with melee and convert Villagers into fellow Cybermen. They also attack Daleks, which have more of an advantage, as they have laser weapons which cause more damage. They drop 1-4 Steel Ingots upon death. All variants of Cybermen have a health of 20.
Classic Cybermen - Appear in Earthshock, Attack of the Cybermen, The Five Doctors and Silver Nemesis
Tenth Planet Cyberman - Appear in The Tenth Planet
Modern Cyberman - Appear in Rise of the Cybermen/Age of Steel, Army of Ghosts/Doomsday, The Next Doctor, The Pandorica Opens, A Good Man Goes to War, Closing Time and (as a puppet for chess) in Nightmare in Silver
Cyber Leader - Appears in The Next Doctor and Blood of the Cybermen (Boss in 1.7)
Cyber Villager - Converted villager.