According to Einstein, a warp drive is a bubble of curved spacetime. Inside this bubble, the ship floats without stress, while the shell ejects a stream of radiation, ordinary light or gravitational waves, at the speed of light. This exhaust pushes the drive forward or sideways, like a boat from which you throw stones. It was once thought that maneuvering was impossible without exotic matter with negative energy. Now it's clear: ordinary radiation is enough. The cost is a huge loss of mass: to make a sharp turn at near-light speed, you'd have to burn up almost half the ship. The warp drive remains slower than light, but it's entirely real. The key discovery is that steering a spacecraft comes down not to mythical matter but to an astronomical energy bill.
To make a sharp turn at near-light speed, the ship must eject almost half its mass, like a car that, at an intersection, sheds its engine, wheels, and body just to change direction.
In Star Trek, captains never worried about fuel; new research shows that even without exotic substances, flight is possible: it's just that the energy budget goes through the roof.