30th century

The Earth Empire fell late in the 30th century, (TV: The Mutants) as a result of exhausting a great deal of time and resources into the war with Verno. (COMIC: Space War Two) By this time Overcities, large tower blocks the size of cities, had large anti-grav engines which allowed them to hover over the undercities. (PROSE: Original Sin)

In the late 30th century, the Black Hole of Tartarus presented a hazard to spacecraft. (TV: Terror of the Vervoids)

The standard of craftsmanship in the century may have been very high, as the Fourth Doctor estimated that the later interior of the Nerva Beacon had originally been built in the late 29th or early 30th century. At the time he made this judgment, it had been left mostly alone for at least ten thousand years. (TV: The Ark in Space)

A force of Cybermen left this century in a time machine and landed on Earth in 1939, only for their invasion to be disrupted by the outbreak of World War II. The Seventh Doctor described their methods of time travel as "still not up to much" even by the 30th century. (PROSE: Illegal Alien)

The First Doctor, John and Gillian prevented the Kleptons from conquering the Thains. (COMIC: The Klepton Parasites)

A Renegade Dalek force (from approximately the 30th century, according to the Seventh Doctor) and an Imperial Dalek faction arrived in Shoreditch in 1963. (TV: Remembrance of the Daleks)

On Solos, Solonians started to mutate into their insectoid phase as their planet experienced summer. (TV: The Mutants)

By the mid-30th century, humanity had completely mapped out the Spiral Head Nebula. (COMIC: The Ghost Ship)

A lurgy swept through the solar system in this century. Iris Wildthyme caught the lurgy and came to Holby Space City to be cured. She met a professor who created clones of himself and Iris and sent them inside Iris' body to cure her. Afterwards, he gave Iris his robotic panda PAND-R. (PROSE: From Wildthyme with Love)

Behind the scenes
The Discontinuity Guide takes the Seventh Doctor's words that the Supreme Dalek was "a thousand years from a disintegrated home" literally, while supposing that it is more likely in the future than the past, and so states that Skaro was destroyed around the 30th century in the new timeline where Davros survived, whereas Skaro was known to exist later in the old timeline.