Star Trek Discovery is two weeks away from returning to CBS All Access for its third season, but the show's first season began airing on CBS last week. Viewers coming to the series for the first time may wonder when Star Trek: Discovery takes place in the Star Trek timeline. While this answer changes in the coming season, Discovery's story begins a decade before Star Trek: The Original Series. Yes, the show looks shinier than The Original Series, but that's because the way people make television changed in the 50 years of real-world time that separate TOS and Discovery's debuts. To answer another question, Discovery takes place in the same universe as every other Star Trek TV show and not in the timeline of the new Star Trek movies.
To put Discovery's place in the timeline into perspective, Star Trek: Discovery's first two episodes occur in the year 2256. That's a decade before Captain Kirk's five-year mission, roughly 150 years before Star Trek: The Next Generation, and 100 years after Captain Archer's journey in Star Trek: Enterprise.
In 2256, there are three major powers in the galaxy: the United Federation of Planets, the Klingon Empire, and the Romulan Star Empire. To give you a sense of what the political landscape looks like, here's what's happening with each of these factions as Star Trek: Discovery begins:
The United Federation of Planets
At the time that Star Trek: Discovery, the Federation of Planets is less than a century old. For being such a relatively young galactic power, the Federation is surprisingly capable of holding its own against its rivals.
The Federation consists of several non-human member races. The most powerful of them would be the founders, including Vulcans, Andorians, and Tellarites.
The Federation by now has encountered unfriendly species during explorations, including the Klingons and the Romulans. However, the events of the Temporal Cold War and the Earth-Romulan War are well behind them.
The Klingon Empire
The Klingon Empire has been around for hundreds of years, making it an ancient establishment compared to the Federation. The Klingons don't get along well with any of their galactic neighbors, including the Romulans.
Relations between the Klingons and Earth got off to a rough start, as seen in Star Trek: Enterprise. By now, there's been a long period of little to no contact between the Federation and the Empire, which makes their meeting in Discovery's premiere a surprising turn of events.
Without a clear threat to unify them, the Klingon houses have fallen into factionalism and infighting. It is a shadow of the mighty Empire it once was and that longtime Star Trek fans know it will become again.
The Romulan Star Empire
During the 2250s, the Romulans are still regrouping after their surprising defeat during the Earth-Romulan war, which established the neutral zone barrier between Romulan and Federation space. They'll be strong and confident enough by the time of The Original Series to begin launching attacks on Federation outposts, but they're quiet for now.
In the meantime, the Romulans are developing their cloaking technology. They will also soon make a significant arms trade agreement with the Klingons. The Romulans don't play a direct role in Discovery (they get the spotlight in Star Trek: Picard), but the threat they pose looms in the background.
Star Trek: Discovery airs Thursdays at 10 p.m. ET on CBS.