A time warp is a phenomenon which can allow travel through time. Usually only formed through great expenditures of energy, a time warp can be created both naturally and artificially (See: Slingshot effect).
In 2266, while spiraling down toward planet Psi 2000, the USS Enterprise traveled back in time three days, after accidentally creating a time warp through an experimental intermix formula which posited a relationship between time and antimatter. (TOS: "The Naked Time")
In 2267, brief time warp distortions were felt throughout the Milky Way Galaxy and beyond, as a result of the magnetic effect created when Lazarus and anti-Lazarus emerged from the alternative warp. (TOS: "The Alternative Factor")
In 2269, the disappearances of many starships in the Delta Triangle region of the galaxy were found to be caused by naturally occurring time warp vortices. The time warps were caused by a small parallel time continuum, known as Elysia, touching the prime universe in that region. The time barrier between the universes was disturbed and nearby starships were pulled into the alternate universe through the vortices. (TAS: "The Time Trap")
In 2286, Spock had to make exact computations for the time warp that brought the HMS Bounty back in time to 1986 using the slingshot effect. Because of the energy required to enter time warp the B'rel ran out of juice and the dilithium crystal chamber was drained. Kirk had to send Chekov and Uhura to steal uranium from the aircraft carrier USS Enterprise (CVN-65). The operation was a success and the Bounty was refueled, but Chekov was captured. For the journey back to 2286, Spock used the first journey through time as a reference, calculating the coefficient of elapsed time in relation to the acceleration curve. Though he had to make a guess, since the additional mass of water and the humpback whales could not be determined exactly, which meant that this variable to the acceleration could not be calculated exactly. (Star Trek IV: The Voyage Home)
In 2372, a Ferengi shuttle carrying Quark, Rom, and Nog, traveled through a time warp when, in an attempt to shut down a sabotaged warp drive, Rom vented plasma from the warp core into the cargo hold, starting a cascade reaction in kemacite being stored there. He then modulated the reaction to create an inversion wave in the warp field, to force the ship into normal space. Although his plan succeeded, it also had the effect of transporting the shuttle back in time to the year 1947. The three Ferengi were able to return to their own time by harnessing the beta radiation from a nuclear explosion to trigger another cascade, causing a temporal surge in the subspace continuum, recreating the same kind of time warp, bringing them back to the present. (DS9: "Little Green Men")
A year later in 2373 the Borg invaded Earth and started the Battle of Sector 001. The USS Enterprise-E destroyed the Borg cube but the Borg escaped in a sphere and fired chronometric particles at the planet creating a temporal vortex. The Enterprise followed the Borg to 2063 and stopped them from altering the timeline by preventing the Phoenix from launching on Zefram Cochrane's Warp Jump and Humanity's first contact with Vulcans. The Enterprise crew restored the timeline and eliminated the Borg and watched events as they happened. (Star Trek: First Contact)