(covers information from several alternate timelines)
|The quadrants of the Milky Way|
| The Alpha Quadrant is located in the upper left|
(click to navigate)
The Alpha Quadrant was the common designation for one-quarter of the Milky Way Galaxy. It was adjacent to the Beta Quadrant and the Gamma Quadrant. One-quarter of the galactic core was located in this quadrant. (Star Trek: Voyager, Season 7 production art;  Star Trek Into Darkness display graphics)
In late 24th century interstellar politics and diplomacy, the four great powers in the Alpha Quadrant were the United Federation of Planets, the Cardassian Union, the Klingon Empire, and Romulan Star Empire, though majority of the territory held by the latter two was found in the Beta Quadrant. Other powers at the time were divided into two groups. The mercantile powers, like the Ferengi Alliance, traded with the great powers. The isolationist powers, like the Breen Confederacy and the Tholian Assembly, defended their territory aggressively and would, on occasion, battle with other powers. (Star Trek: The Original Series; Star Trek: Deep Space Nine; Star Trek Into Darkness display graphics) By the late 23rd century, the Alpha Quadrant still remained largely unexplored by the United Federation of Planets. (VOY: "Flashback")
The Bajoran wormhole connected the Bajoran sector in the Alpha Quadrant to a point near the Idran system on the far side of the Gamma Quadrant near Dominion space. The use of this wormhole for exploration and trade by parties from the Alpha Quadrant incited hostility from the Dominion, culminating in the Dominion War. (Star Trek: Deep Space Nine)
In the alternate 2259, a section of this quadrant, from a galactic map, was in a collection of graphics and video media that were seen on a powerwall in the offices of Admirals Christopher Pike and Alexander Marcus at Starfleet Headquarters. The map was being used primarily for charting activity on the Neutral Zone, Sectors 45 to 89. The three largest powers in this section – the Federation, the Klingon Empire, and the Orion Union – were labeled on this map. (Star Trek Into Darkness)
- Breen Confederacy
- Cardassian Union
- Ferengi Alliance
- Klingon Empire
- Romulan Star Empire
- Tholian Assembly
- United Federation of Planets
- Other timelines/realities
- Klingon-Cardassian Alliance (mirror universe)
- Terran Empire (mirror universe)
- Orion Union (alternate reality)
- Cardassian Empire (alternate timeline)
- Barzan II
- Bolarus IX
- Cardassia Prime
- Earth (Sol III)
- Pollux IV
- Talos IV
Alpha/Beta quadrant border
The Star Trek Encyclopedia (2nd ed., p. 393) states that the Federation was spread across the Alpha and Beta Quadrants, with Earth as the border between, in order to explain why the USS Enterprise was often the "only ship in the quadrant", though the term quadrant has been often used to refer to smaller segments of the galaxy as well. The maps in the Star Trek: Star Charts also use Earth as the border between the Alpha and Beta quadrants.
Graphics used in astrometrics for Star Trek: Voyager, starting with the episode "Year of Hell", and on a PADD on Picard's ready room desk in Star Trek: Insurrection, also have Earth and the Federation straddling the border between the two quadrants. 
Dialogue in Star Trek: Deep Space Nine and Star Trek: Voyager, however, firmly establish that Earth is located on the Alpha Quadrant side of the border. Graphics used in Star Trek: Discovery and the alternate reality films support this, where the Alpha/Beta Quadrant border is moved one sector "west" and a star chart graphic used in Star Trek Into Darkness had the label "Alpha Quadrant" near Sector 01 (Level 3-B), which contains Earth. 
According to the Star Trek Encyclopedia (2nd ed., p. 393), Federation, Klingon, and Romulan territories are situated in both the Alpha and Beta quadrants. Dialogue from Deep Space Nine and Voyager exclusively referred to all three powers and governments in their vicinity as Alpha Quadrant powers.
In most reference works, novels, and games, Klingon and Romulan space are usually depicted or stated to be located solely in the Beta Quadrant. This would make the Federation the only government spanning both quadrants.
The video game Star Trek Online is largely faithful to the Star Charts representation of the galaxy, with a few systems moved for gameplay considerations.
According to the Star Charts, most of the early voyages of Enterprise NX-01 took place in the Beta Quadrant with only a few excursions in the Alpha Quadrant.