Warp field
A warp field, also known as the subspace displacement field or the subspace warp field, was the means by which a warp drive propelled a starship at faster-than-light (or warp factor) speeds. Generated by field coils, usually found in nacelles, the field surrounded the ship, causing the space around the ship to distort by the creation of a warp bubble. 

The warp field, also known as a subspace field, was a subspace displacement which warps space around the vessel, allowing it to "ride" on a distortion and travel faster than the speed of light. () This had the physical effect of reducing the inertial mass of any object encompassed by the field. (; )

During emergency situations where the transfer of crew or other objects is necessary while in warp, the warp fields of two vessels may be brought into contact with each other and merge to form one, provided both ships remain motionless relative to each other and at the same warp velocity. ()

Creating an inverse warp field was analogous to dropping the anchor for a starship.  used such a field in 2376 in an attempt to ride out a massive neutronic wavefront impacting its shields at a velocity of two hundred thousand kilometers per second. The warp core needed to be converted before the field could be generated. ()

The warp field of a Federation starship like the  left behind an electromagnetic signature on Data's internal servo fluid system. ()

The interactions between a warp field and a wormhole could be unpredictable, and ships routinely dropped to impulse when traveling through one. In 2370, a plasma injector leak aboard the runabout Rio Grande caused the vessel to enter the Bajoran wormhole with an only partially-collapsed warp field. This had the effect of transporting the runabout, along with its two crewmembers, Major Kira Nerys and Doctor Julian Bashir, to a parallel universe. Kira and Bashir were later able to return to their own universe by recreating the accident and going back through the wormhole. ()

In 2063, Geordi La Forge was able to modify the warp field of the  to match the exact chronometric readings of the Borg sphere they had pursued back in time and was able to recreate the temporal vortex that the sphere had created and return the Enterprise to the 24th century. ()

Warp fields can be disrupted by inverse graviton bursts. In 2375, the , under the command of Dahar Master Kor, managed to destabilize the warp fields of several pursuing Jem'Hadar attack ships by using the technique. () 

The warp fields of conventional warp engines caused damage to the fabric of spacetime where subspace was unstable, eventually causing subspace to extrude into normal space, creating phenomena such as subspace rifts. In order to slow the rate of damage, the Federation Council shared their findings with all known warp-capable species in 2370 and imposed a speed limit of warp factor 5 on all Federation vessels in all but extreme emergencies. () 

Destabilized Omega molecules destroy subspace through rupturing it on such a vast scale that it impossible to create a stable warp field in the area. ()

Configurations
Broad-spectrum warp field
Rentrillic trajectory
Static warp shell
Symmetric warp field

See also
Warp particle

Background information

While it has never been canonically clearly stated exactly how the warp field works, several statements and displays have been made and used over the course of the series:
The warp core is a gravimetric field displacement manifold. ()
The warp coils create a subspace displacement field. ()
An object not entirely encompassed by the forward end of the warp field may be destroyed by subspace compression. ()
Several displays in engineering on the Enterprise-D show radiating lines emitting from the warp nacelles. These lines are tightly spaced in the front of the saucer while widely space at the rear, to the point of another whole ship length. (TNG)
These lines correspond with lines seen on a display showing the warp fields of  and . ()

According to the Star Trek: The Next Generation Technical Manual, the space-time continuum distortion based propulsive effect of a warp field is created by nesting several layers of warp field energy together, with each new layer exerting force against its outermost neighbor. The cumulative effect of this force results in the massive subspace field distortion that allows the ship to reach faster than light speeds. (p.54) The shape of the warp field produces the propulsive effect. (p.64) The forward lobe of the field is created with a frequency offset to create the field shape asymmetry required to drive the ship forward. (p.65)

de:Warpfeld
fr:Champ de distorsion
ja:ワープ・フィールド
Warp
Energy fields