Cybermen in popular culture and mythology

Due to their expansionist, warmongering tendencies, the Cybermen were known far and wide across the universe, including on Earth, where, by the 21st century, accounts of them existed not only as matters of historical fact, but as fictional antagonists and as "the stuff of legend", in much the same way as their long-standing enemy the Doctor did.

As real beings
In the late 20th century, the Cybermen, led by a Cyber-Planner that recognised the Doctor from Planet 14, launched an invasion of Earth, aided by Tobias Vaughn of International Electromatics. However, this invasion was thwarted by the Second Doctor and the newly formed United Nations Intelligence Taskforce, led by Brigadier Alistair Gordon Lethbridge-Stewart, who saw that the Cyber-Fleet was destroyed. (TV: The Invasion)

In December 1986, the Cybermen of Mondas introduced themselves to humanity as they landed on Earth in an invasion, which ended with their defeat and the destruction of Mondas. (TV: The Tenth Planet)

In 2007, an army of Cybermen from a parallel Earth, named Pete's World, crossed over and invaded the Earth of N-Space, beginning with an advance guard planted within Torchwood Tower at Canary Wharf in London. Though the Torchwood Institute had been working to defend the British Empire from aliens since 1879, Torchwood One director Yvonne Hartman was unfamiliar with the Cybermen until this encounter. (TV: Army of Ghosts) Taking control of Torchwood's ghost shifts, Cyber-Leader One saw the full transfer of five million Cybermen from their homeworld, appearing across Earth including in London, Paris, Delhi (TV: Army of Ghosts) and Spain. (TV: The Runaway Bride) In a global broadcast from Torchwood Tower, the Cyber-Leader ordered the surrender of all humankind only to be met with armed resistance, beginning the Battle of Canary Wharf, a battle which was ended within the day as the Tenth Doctor pulled the Cybermen back into the Void from which they came. (TV: Doomsday)

Following the battle, some refused to accept the existence of alien life, to the confusion of Jack Harkness, who cited the battle with a "Cyberman in every home" to Gwen Cooper. Gwen noted that her boyfriend, Rhys Williams, believed such appearances to be a result of mass hallucinations caused by psychotropic drugs planted in the water supplies, a theory which Jack called "stupid". (TV: Everything Changes)

Michael Hamilton continued to see Cybermen outside of his mother's house. (TV: Greeks Bearing Gifts)

By 2009, many people had become aware of alien life through the Cybermen and the Daleks. (TV: The Mad Woman in the Attic)

In 2012, an invasion of Earth by the Cybermen, which involved the Doctor, was recorded on the internet. (COMIC: Invasion of the Mindmorphs)

In 2070, Jack Hobson claimed that every child knew the Cybermen, but that they were all destroyed ages ago. (TV: The Moonbase)

In the 25th century, the Brotherhood of Logicians searched the universe for the last remains of the Cybermen, who were by that point believed to have died out five hundred years prior. (TV: The Tomb of the Cybermen)

Novels by Sarah Jane Smith
After she ceased being a companion of the Doctor, Sarah Jane Smith published a number of books adapted from her experiences as a time-and-space-traveller, which were billed as science-fiction novels on Earth.

Among these was Return to the Ark, a part of her Doctor series in which a fictionalised version of the Doctor was featured as main character. (PROSE: Moving On)

As a complete unknown
Londoner Rose Tyler, who joined the Ninth Doctor in the TARDIS in March 2005, (TV: Rose) was initially unfamiliar with the Cybermen, her first encounter being with a inactive specimen in Henry van Statten's vault. (TV: Dalek) Through this sight, she recognised the Cybermen in Pete's World. (TV: Rise of the Cybermen) Rose's mother, Jackie Tyler, remained ignorant of the Cybermen until they crossed over to N-Space during the Battle of Canary Wharf. (TV: Army of Ghosts)

The Eleventh Doctor observed that the CyberKing, "a giant Cyberman walk[ing] over all of Victorian London" on Christmas 1851, was not remembered. He found reason to believe that the memory of its appearance was erased by a crack in time. (TV: Flesh and Stone, The Next Doctor))

In 2011, Colchester resident Craig Owens did not recognise a Cybermen which appeared much like those that appeared during the Battle of Canary Wharf. (TV: Closing Time)

Sheffield residents Graham O'Brien, Ryan Sinclair and Yasmin Khan, who joined the Thirteenth Doctor in September 2018, (TV: The Woman Who Fell to Earth) were unaware of the Cybermen until they were told of them by Jack Harkness. (TV: Fugitive of the Judoon)

In 2079, Jarvis Bennett failed to recognise the Cybermen. (TV: The Wheel in Space)

Other realities
In the year 2059 of an alternate timeline created by the erasure of Rani Chandra's friends in 2009, she recalled to Adam Lloyd that people were already aware of aliens back then through the Cybermen and the Dalek, but were yet to know "everything". (TV: The Mad Woman in the Attic)

On Gallifrey and among Time Lords
By the end of their second incarnation, the Doctor, via a Thought Channel, cited the Cybermen among the evils he had fought as he stood trial for defying the Time Lords' non-interference policy. Conjuring an image of Cyberman, the Doctor described them as "half creature, half machine" as he condemned the Time Lords' inaction. Ultimately, the Time Lords accepted his plea that there was evil in the universe that must be fought, and that he still had a part to play in that battle, resulting in his forced regeneration and exile to Earth. (TV: The War Games)

While on Telos, the Sixth Doctor suspected that the Time Lords had manoeuvred him into thwarting the Cybermen's attempt to use Halley's Comet to destroy Earth in 1985 and so avert the destruction of Mondas in 1986, which would have violated the Web of Time. (TV: Attack of the Cybermen)

Others
Following the Last Great Time War, Dalek Sec of the Cult of Skaro identified the Cybermen as an "inferior species" to the Daleks. He identified the outline of those from Pete's World as "[resembling]" the Cybermen. (TV: Doomsday)