26th century

In the 26th century, the first Earth Empire formed from an Earth-centred alliance of planets. It lasted until the late 30th century. Earth's single, planet-wide government was called EarthGov. (PROSE: Missing Adventures: Home)

Tensions existed between the Earth Empire and the Empire of the Draconians and even more so with the Daleks and the Korven. (TV: Frontier in Space, The Korven)

Earth's Moon was used as a penal colony. (PROSE: Home)

Thanks to genetic engineering, humans no longer had wisdom teeth. (PROSE: Dry Pilgrimage)

The Second Dalek War took place. Many planets were destroyed in the conflict. The war ended when the Tenth Doctor and the crew of the Wayfarer destroyed the Dalek ship Exterminator and its Dalek crew, leaving its leader, Dalek X, for dead. (PROSE: Prisoner of the Daleks)

By mid-century, much of what had been the southern United States had sunk under the "Mississippi Sea" — probably a much-expanded Caribbean Sea. (PROSE: Home)

Space travel became relatively commonplace and affordable, though trips could be lengthy. It was common to sedate passengers for the longer trips. (PROSE: Biology Lesson on Mal Oreille)

The Sontarans and the Rutans took their war to Chelsea 426. The Tenth Doctor stopped the Rutans and the Sontarans left before the colony collided with a Great White Spot. The Doctor prevented this as well. (PROSE: The Taking of Chelsea 426)

Space travel appeared to be significantly faster by the end of the century; the approximately twenty-seven thousand light-year trip from Earth, near the edge of the galaxy, to Dellah, near its core, took about eleven months. (PROSE: Oh No It Isn't!)

Notable individuals
Bernice Summerfield grew up in this century. (PROSE: Just War)

Abslom Daak and the Star Tigers fought Daleks at this time. (COMIC: Abslom Daak... Dalek Killer)

Ace lived here for three years when she decided to leave the Seventh Doctor and join Spacefleet. (PROSE: Deceit)

Laura Tobin lived in this century as a human before her transformation into the Eighth Doctor's companion Compassion. (PROSE: Interference - Book One, Interference - Book One)

Space Major Jon Bowman lived in this century. He was in charge of a starship with a crew of bounty hunters during the Second Dalek War, which he helped the Tenth Doctor to end. He and another member of his crew, Koral, survived. The other three died. (PROSE: Prisoner of the Daleks)

Alternate timeline
In a potential history shown by the Eleventh Doctor to Jean-Luc Picard, the Cybermen, having integrated both the Doctor's N-Space and Picard's parallel universe before conquering the Borg, concluded their campaign to convert the galaxy by crushing the last holdout of free humanity on Earth. (COMIC: Assimilation²)