31st century

The 31st century was defined in the calendar of Earth as being from 3001 until 3100.

Events

Earth 31st Century — A devastated San Francisco in the 31st century of an alternate timeline, where the United Federation of Planets never came into being

Daniels is born. By this time, time travel is so commonplace that there are quantum discriminators in every high school desk. (ENT: "Shockwave, Part II")
Circa 3052: Daniels, fearing a change in the timeline, transports Jonathan Archer to this time, causing a catastrophic timeline change that wipes out his entire civilization. Returning Archer to 2152 remedies the problem. (ENT: "Shockwave", "Shockwave, Part II")
Circa 3052: A time travel pod travels back to the 22nd century, where it apparently suffers some sort of critical disaster. The pilot is killed in the accident and the pod itself is heavily damaged. It is eventually discovered by the Enterprise NX-01 in October 2152, and Enterprise's chief engineer Commander Charles Tucker is able to reactivate the pod's temporal beacon. Within seconds, the pod, the dead pilot, and the beacon itself all vanish, having presumably being retrieved by operatives from the 31st century. (ENT: "Future Tense")
Circa 3070: Captain Jean-Luc Picard estimated that the core of Atrea IV would remain molten for seven hundred years. (TNG: "Inheritance")
Circa 3074: In the Delta Quadrant, a Kyrian historian named Quarren discovers a back-up copy of The Doctor. After he is reactivated, The Doctor corrects the distorted view of USS Voyager in Kyrian history and precipitates a new harmony between the Kyrian and Vaskan races. After many years as Kyrian Surgical Chancellor, this copy of The Doctor boards a ship and heads for the Alpha Quadrant to find out what happened to Voyager and his fellow crewmates. (VOY: "Living Witness")

Background information

This is the last year depicted in Star Trek canon. "Living Witness" does go farther into the future, but without a date or time frame specified.

Kyrians obviously have had no contact with the Federation between their encounter with Voyager in 2374 and this time, despite claims by Q that the Federation will have a presence in the Delta Quadrant as soon as the late 25th century as per VOY: "Death Wish".

Going by Data's statement that the The energy ribbon from Star Trek Generations passes through the Milky Way Galaxy every 39.1 years, it can be expected to return in 3034 and 3073.

The undeveloped series Star Trek: Federation would've taken place in this century.