67th century

The 67th century, according to the Thirteenth Doctor, was a lovely century — "a bit tricky in the middle, but it's alright in the end." When reminded about the complexity of the technology of this time, she regretted not having visited this century more often. (TV: The Tsuranga Conundrum)

The Thirteenth Doctor, Graham O'Brien, Ryan Sinclair and Yasmin Khan visited Seffilun 27 during an unknown year in the 67th century. They were incapacitated by a sonic mine, then rescued and treated aboard the hospital ship Tsuranga, which came under attack by a Pting. (TV: The Tsuranga Conundrum)

By the 67th century, a large portion of our galaxy was still recovering from the devastation of the Great Catastrophe. Spaceship technology had returned to the point of interstellar ships with solar sails, plus the occasional standard warship.

The central inhabited part of the galaxy (including, presumably, Earth) was ruled by the Galactic Union, while the outlying areas had banded together into the Confederation of Border Worlds.

As part of a plan for re-invasion of the galaxy, the Daleks seeded the Border Worlds with the NFS plague. Once the Border Worlds were suitably isolated from the Galactic Union, the Daleks offered to help cure the plague, setting up healing zones on various geo-formed planets.

Siy Tarkov, a Galactic Union envoy, visited the planet Velyshaa and obtained records of the previous Dalek War and the resulting Great Catastrophe. Those records were eventually transmitted to the Galactic Union, informing them of the imminent threat of Dalek invasion. (AUDIO: Dalek Empire III)