Of the many fictional and theoretical Faster Than Light (FTL) travel methods, Warp differs in that it does not instantaneously take you to your destination. In order to travel faster than light, you either have to bend space itself to create a wormhole or change your own mass to be lighter than that of a photon (which is close to massless). Warp Drives utilizes the latter.
In Star Trek it is described as a bubble around the ship that warps the space around the ship, rather than the ship itself, thus allowing the ship to be virtually massless. Thus the so-called time barrier is broken, and no time dilation occurs for the ship (time dilation is when time moves slower for things objects move closer to the speed of light relative to objects that move slower).
This fictional method of propulsion was first introduced in the novel Islands In Space by John W. Campbell in 1931. It was most famously adopted in Star Trek: The Original Series and has been used in every Star Trek series and film since then. But is such a thing possible?
In 1994, physicist Miguel Alcubierre theorized that a field of energy-density lower than vacuum could be created and this would create negative mass, allowing for warp speeds. Using this method, called the Alcubierre Drive, one would not move through space in a local frame of reference, but instead contract space in front of the craft and expanding it again behind the craft. Later calculations proposed this would require exotic matter to fuel it. Exotic matter is matter that is not constructed with protons and electrons, but some other exotic subatomic particles.
If such matter were to be discovered, the drive would be theoretically possible, as it does not conflict with Einstein’s field equations.
In 2012, NASA researcher Harold White theorized that it would be possible to build a Alcubierre Drive, if the shape of the drive and the field were changed from the originally proposed one. NASA is currently researching the technology and the preliminary research has been promising. We might have Warp Drives in the near future.