Warp drive is a technology allowing faster-than-light travel through space, creating warp fields and forming a subspace bubble surrounding a starship, which, in turn, forms a distortion in space-time and allows the starship's movement to exceed the speed of light. The rates of movement above the speed of light are known as warp factors.
As different manifestations of the same general force, gravitational forces can be manipulated by applying precisely-controlled electromagnetic forces. Electromagnetic forces, therefore, can alter spacetime's geometry as gravity is simply a curvature of the latter. Warp drive alters spacetime's fabric, allowing the vessel to attain warp velocities.
In most known starships, a matter-antimatter reaction creates high-energy plasma. The plasma, in turn, flows through several warp coils, which are comprised mostly of verterium cortenide, an artificial material. This material bridges gravitational and electromagnetic forces, and, when shaped correctly, high-energy plasma can flow through it and create a "warp field". The interaction between the two can alter spacetime's geometry near and around the warp nacelles, creating multilayered waves of warped timespace, allowing the ship to jump to "warp" and cruise at a velocity greater than the speed of light. The ship itself, within the "warp bubble", does not travel faster than the speed-of-light as the area within the bubble is a pocket of "normal" space; therefore, the laws of physics are not broken. 
With the starship stationary within the warp bubble, exceeding the speed of light is possible, with spacetime itself (surrounding the warp bubble) moving. The occupants and starship do not experience any alteration to the normal passage of time, as time within and outside the bubble are the same (under normal circumstances).
A reaction between deuterium and antideuterium, tempered through a dilithium crystal assembly, allows 24th century Federation vessels to travel at warp speeds. Dilithium does not react with antimatter when high-frequency electromagnetic fields come into play. The reaction between the deuterium and antideuterium creates electro-plasma, a highly-energetic plasma. Magnetic conduits deliver the electro-plasma to the plasma injectors via the electro-plasma system (EPS). Once at the plasma injectors, the plasma flows into a series of field coils; these coils are usually housed in the warp nacelles aboard the ship.
Other civilizations, like the Romulans, utilize other power sources. In the case of the Romulans, this is an artificial quantum singularity. Overall, the basic process remains very similar amongst all warp-faring nations.
Some Federation Starfleet starships, like the Intrepid-class and Aotearoa-class have nacelles whose geometry can be altered via moveable pylons, allowing these types of starships to travel faster and damage subspace less (or not at all). Newer Starfleet ships, like the Sovereign-class, have had this issue addressed through redesigned nacelles, eliminating the variable-geometry pylons while allowing the faster velocities.
Parts of the system
- antimatter containment
- antimatter relay
- deuterium cartridges
- magnetic conduit
- magnetic interlock
- nullifier core
- phase inducer
- plasma conduit
- plasma injector
- plasma intercooler
- plasma regulator
- power transfer conduit
- power transfer grid
- warp plasma conduit
- warp coil
- warp core
Cultures throughout the galaxy discover warp drive at different times. The Vulcans are known to have utilized warp drive as early as Earth's 3rd century; however, the Vulcans lost this ability during a planetary civil war, and they did not gain the capability again until several centuries later. By 2151, Vulcan warp drives could reach warp 7. (ENT: "Kir'Shara") Klingons, on the other hand, could travel at warp 6 in the same year, although not much is known about when they first became warp capable. (ENT: "Judgement") Humanity's gaining warp capability in the 21st century fostered a renaissance of exploration in the Milky Way Galaxy and fostered the formation of the United Federation of Planets.
Warp drive makes interplanetary trade and exploration possible. For example, Vulcan is approximately 16 light years from Earth. At 2270's top impulse speeds (warp factor 0.8), this journey would take 20 years between the two planets. At warp speeds, this same journey could take as little as 4 days. (Star Trek: The Motion Picture)
Earth's Zefram Cochrane developed warp drive on the planet in the years following the disastrous planetary war, World War III. With hardship amongst the planet's people and the lack of advanced materials being generally available, he converted a Titan V missile to contain his warp-capable ship, the Phoenix. On 6 April 2063, Cochrane and a flight crew successfully tested the Phoenix, getting a passing Vulcan exploratory vessel's attention. This event was the catalyst for first contact between Earth and the Vulcans. (Star Trek: First Contact)
Cochrane's original design used nuclear fission, incorporating materials from the Titan V. Later developments of matter-antimatter reactors in later years would create more stability amongst the systems and allow humans to utilize it to its full potential.
- At least one account asserts that a parallel effort to develop warp drive took place in the Eastern Coalition during the 2050s and 60s. A successful launch from the Baikonur Cosmodrome occurred in January, 2063 -- three months before Zefram Cochrane's -- but remained unknown to the world outside the Coalition. (Advanced Starship Design Bureau: Journal of Applied Treknology: "Molniya Class")
Despite humanity's great leaps and bounds in warp technology during the middle of the 21st century, the next 80 years brought very few changes. During the 2140s, Henry Archer created a warp engine able to break the "warp 2 barrier". Commanders A.G. Robinson and Jonathan Archer tested the engine in the second NX prototype, achieving warp 2.5 during the test. (ENT: "First Flight")
The warp 4 barrier was broken by the USS Franklin in the 2140s (Star Trek Into Darkness), and by 2151, some human starships could achieve warp 5: the starship Enterprise was one. (ENT: "Broken Bow") After its initial launch, Enterprise could only reach a maximum of warp 4.7, but, on 9 February 2152, it gained the ability to travel warp 5. (ENT: "Fallen Hero")
- In at least The Starfleet Museum continuity, Earth's early warp-driven starships were powered by nuclear-fusion reactors. In 2152, the SSWR-IA matter/antimatter reactor was certified for use aboard starships. (The Starfleet Museum: Museum Timeline)
Between 2236 and 2254, the Federation made a major breakthrough in warp technology, breaking the "time barrier". This allowed Starfleet ships, such as those of the Constitution-class, a warp 6 cruising speed and emergency speeds up to warp 8. In some rare circumstances, vessels could even reach warp 9. (TOS: "The Cage")
Alien interventions or dangerous malfunctions saw warp speeds increase. The Kelvans modified the USS Enterprise's warp drive to achieve warp 11 in 2268, and, a few months later, an alien entity named Losira sabotaged the Enterprise, nearly tearing the ship apart at warp 14.1. (TOS: "By Any Other Name", "That Which Survives")
Starfleet redesigned the warp engine, and the Corps of Engineers replaced the cylindrically-shaped warp nacelles with a flatter, more rectangular design aboard Constitution-class refits during the 2270s. These new designs allowed for standard speeds of warp 8 and higher. (Star Trek: The Motion Picture)
Starfleet also experimented with a new type of warp drive called transwarp during the 2280s. The theories behind this drive included greater efficiency and attaining higher warp velocities. Starfleet tested this failed technology aboard the USS Excelsior but deemed them unsuccessful. (Star Trek III: The Search for Spock) The Excelsior gained a conventional warp drive and continued to serve Starfleet. (Star Trek VI: The Undiscovered Country)
Sometime between the 23rd and 24th centuries, a new warp factor scale was created and used. With the original design based on a cubic power scale, the new scale worked exponentially, with warp 10 allowing a ship to be at infinite places and infinite times. (TNG: "Encounter at Farpoint"; VOY: "Threshold"; TNG novel: Indistinguishable From Magic)
By 2364 and the launch of the Galaxy-class USS Enterprise-D, warp drives could sustain warp 9.6 for 12 hours; however, many engineers believed warp 9.2 was the "red line". (TNG: "Encounter at Farpoint")
The Federation Council set a speed restriction of warp 5 after Hekaran scientist Serova revealed warp drive damaged spacetime. The limit could be broken in extreme emergencies. (TNG: "Force of Nature", "Eye of the Beholder")
The Corps of Engineers came up with a solution within eight months, adapting all vessels' warp drives to once again utilize maximum warp velocities. Some ships, like the Intrepid-class, were outfit with variable-geometry warp nacelles, while other ships, like the Sovereign-class, were fit with new nacelle designs from their launch. (VOY: "Caretaker"; Star Trek: First Contact)