21st century

The 21st century was, as Jack Harkness cryptically said, "when everything changes". (TV: Everything Changes) Among other things, the early 21st century was when the whole human race on Earth learned that alien life existed. (TV: The Christmas Invasion)

Earlier chronicled invasions, including those of the Yeti (TV: The Web of Fear) and the Slitheen family (TV: Aliens of London/World War Three), were believed by the general public to have been hoaxes, or otherwise covered up. (TV: Remembrance of the Daleks, World War Three) Others, such as the Racnoss invasion (TV: The Runaway Bride), the disappearance of Royal Hope Hospital (TV: Smith and Jones) and the March of the Adipose (TV: Partners in Crime) were brief in duration.

Most alien encounters, such as the common incursions through the Rift (TV: Everything Changes, Day One, Combat, End of Days, Kiss Kiss, Bang Bang, et al.) and conspicuous alien presences in Ealing (TV: Invasion of the Bane, Revenge of the Slitheen, Eye of the Gorgon, Warriors of Kudlak, et al.), though well-known enough to lead to the area being dubbed "the Ealing Triangle" (TV: Goodbye, Sarah Jane Smith), were insignificant. However, as alien incursions became more frequent, it became harder to dismiss them, especially the worldwide invasions such as the Battle of Canary Wharf in 2007 (TV: Doomsday) and the Dalek Invasion of Earth in 2009. (TV: The Stolen Earth)

The government publicly opened negotiations with the alien race the 456 in 2009. (TV: Children of Earth: Day Three) Earth was a very tempting target for invasion; by 2009, half of the species from Earth to the Verlixix Spiral Cluster had plans to invade. (TV: Enemy of the Bane)

Miracle Day also affected Earth in this century. (TV: The New World)
 * In a negated timeline, most people knew and accepted alien life by the 2050s (TV: The Mad Woman in the Attic), although given events early in the century, odds are this fact remains in the restored timeline.

Ashildr, a 9th century Viking girl who was rendered effectively immortal when she was brought back to life by the Twelfth Doctor through a self-repairing Mire repair kit, (TV: The Girl Who Died) was known to have lived on Earth up to at least the early part of the 21st century, by which point she was the Mayor of the trap street. (TV: Face the Raven) She would ultimately live all the way to the end of the universe. (TV: Hell Bent)

Specific events
In 2009, the Earth was moved to the Medusa Cascade by the Daleks, causing untold damage around the world, which nonetheless united in joy when the planet was returned to its proper place. (TV: The Stolen Earth / Journey's End) However, this was then unwritten from time by the Time Field. (TV: Victory of the Daleks, Flesh and Stone)
 * It's left unclear as to whether Big Bang Two (TV: The Big Bang) prevented the unwriting of these events.

This century was a period of great technological advancement, but also great political, economic, and ecological turmoil. The T-Mat (TV: The Seeds of Death) and the weather-controlling Gravitron (TV: The Moonbase) were developed in the middle part of this century, and the first excursions outside the Solar System occurred towards the century's end. (TV: The Waters of Mars)

In an unknown year after 2013, Shakri cubes were sent to Earth to begin the Year of the Slow Invasion. A year later, they absorbed electricity and released it, causing cardiac arrest in millions of humans as part of the Shakri's plot to wipe them out. The Eleventh Doctor reversed the effect of the cubes, restarting the hearts of the survivors of the cubes' attack, and causing one of the Shakri's ships to explode. Amy Pond and Rory Williams, having debated for some time over whether to choose life at home or life with the Doctor, decided to travel with him again. (TV: The Power of Three)

Space travel increased dramatically. Many more missions were undertaken by NASA, the Russian Federal Space Agency, and European Space Agency (later the Eurozone Space Agency AUDIO:The Feast of Axos). All-German teams achieved ten lunar missions by 2050. Australia, Spain, and (possibly) the Philippines all got involved in space travel. The Branson Inheritance (TV: The Waters of Mars) and Ironclad Industries (who bought the British Rocket Group) were two private space organisations. (AUDIO: The Feast of Axos) In 2071, India's space agency collaborated with Britain in clearing space junk out of Earth orbit. (AUDIO: Scavenger) This new space race ended when T-Mat was invented, causing rockets to be seen as obsolete. This was shown to be an error when the Ice Warriors seized control of T-Mat Control (TV: The Seeds of Death) in 2086.(PROSE: Transit)

The nations of Europe began to unify more under the Eurozone. (PROSE: Trading Futures)
 * For forty years after 2019, Earth suffered through climate change (including both extreme storms and a 22+ weeks without rain), ozone degradation, the "Great Cataclysm", and "the oil apocalypse". Millions of refugees streamed out of North Africa and the Baltics. In 2059, it was believed mankind came close to extinction. (TV: The Waters of Mars, TV: Aeolian, AUDIO: Hothouse) People in the future would remember Earth's ecosystem collapsed during this century. (AUDIO: Davros)

In 2049, a dragon-like creature hatched out of the Moon, laying an egg that became the new Moon. (TV: Kill the Moon)

Earth's first off-world colony, Bowie Base One, was both established on Mars and lost in the late 2050s. (TV: The Waters of Mars) It would later establish a permanent base. (PROSE: Home)

The Thousand Day War between the United Nations and Mars was fought between 2086 to 2088, following the T-Mat attack. Over 45,000 UN soldiers were killed and Paris was bombarded in an act of terror, but the weakened Ice Warriors were defeated. Most of the Warriors left Mars for a new planet and humans started to colonise it en masse. (PROSE: Transit, GodEngine, Legacy)

Earth sends its first lightspeed ship to Proxima Centauri, under the command of Susie Fontana Brooke. (TV: The Waters of Mars)

Various nations had political changes during this century: Italy suffered civil war and China split into North China and South China in the early 21st century (PROSE: Trading Futures), Britain become the dictatorship of New Britain for part of the mid-21st century, and the United States fell. (PROSE: Christmas on a Rational Planet)

At some point during this century, on an Istanbul rooftop, the Ninth Doctor fought two Sontarans in a sword fight. Sally Sparrow, who had become "some sort of spy", saved the Doctor from one of them, and gave him her Christmas homework from 2005, which would help him when the TARDIS would later hop forward in time twenty years without the Doctor. Sally told the Doctor to keep the essay with him at all times. (PROSE: What I Did on My Christmas Holidays by Sally Sparrow)

In 2074, the Anti-Grav Olympics were held. (TV: The Bells of Saint John)

Using gold as currency fell out of favour in the late 21st century. (AUDIO: The Evil One)