Info from Narcissus needs to be added
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Part of a group stuck on Earth, the Zygons landed in 1562, but the group retreated into a stasis cube and stayed there until the 21st century. After leaving the stasis cube, now housed at the Under Gallery, one Zygon took Osgood's form after ambushing the real Osgood and took her inhaler. The real Osgood escaped, however, and reclaimed her inhaler while doing so.
Later, three incarnations of the Doctor erased the memories of both the humans and their Zygon counterparts when they took control of the UNIT Black Archive, forcing the two species to negotiate a ceasefire. When the Zygon Osgood suffered an asthma attack, the real Osgood quietly passed over her inhaler, allowing these two to secretly know which was human and which was Zygon. (TV: The Day of the Doctor)
The two Osgoods then created Operation Double, where a group of 20 million Zygons would be allowed to live on Earth and take on the form of the nearest person they could find. The treaty could only be maintained if both humans and Zygons agreed to live among each other in peace, and that no harm would come to anyone. They were given a device called the Osgood Box by the Doctor, to be used only in a dire emergency. (TV: The Zygon Invasion)
After Missy began to deploy her Cyberman army across the world, (TV: Death in Heaven) the Zygon Osgood (AUDIO: Narcissus; WC: The Zygon Isolation) confronted and secured her. She was stationed near Missy during her captivity aboard Boat One, who told Osgood she was planning on killing her. Missy proceeded to count down to Osgood's death, taunting her with each number. She then unlocked her handcuffs, killed her guards and grabbed hold of Osgood. Despite claiming to be more useful to Missy alive, Osgood was vaporised, with only her glasses remaining intact until Missy crushed them under her heel. (TV: Death in Heaven)
After an encounter with the Twelfth Doctor, another Zygon, Bonnie, decided to become an Osgood, taking the place of the one who had died. Neither Osgood would reveal if they were human or Zygon. (TV: The Zygon Inversion)