The speed of light is a limit on the speed of particles moving around within spacetime. However no such limitation applies to how fast space can grow or contract within itself. We see this in action in two separate places: (1) inside a black hole, and (2) with the expansion of the universe itself.
In the case of (1), we see that space itself is contracting so fast at the event horizon of the black hole, that it exceeds the speed of light. In the case of (2), we see that beyond a certain distance from us, galaxies are expanding away from us faster than the speed of light, which is called the Hubble Sphere. The Hubble Sphere is centered around us at a radius of 14 billion light-years, and all galaxies that are currently beyond this distance are expanding away faster than light.
A theoretical warp drive, such as the Alcubierre Warp Drive can get around the light speed limits, by keeping the space ship perfectly still in a pocket of spacetime, and then creating a space compression wave in front of the ship, and a space expansion wave behind it. So the bubble of spacetime in which the craft resides stays perfectly still, and it gets moved along like a surfboard on the waves. One problem with this is, beyond the fact that we have no technology to compress or expand space with yet, is that the beams that will create the compression and expansion, are themselves limited to the speed of light. So a self-contained warp drive will probably take us close to the speed of light, but not beyond it. If you want to go beyond the speed of light, you'll need warp drive projectors sitting on the path in front of you, creating the expansion and compression waves from the outside, so it would be more like a warp-drive railway, rather than a self-contained warp-drive.