In reality, the light from distant objects is redshifted, but not because something is moving away faster than light, nor because something is expanding faster than light. Space is simply expanding; it's us who are moving at a “speed” because that's what we're used to. It's true that in special relativity, nothing can move faster than light. But special relativity is a local law of physics, meaning that you will never see a rocket fly in front of your face faster than the speed of light.
Sutter also hosts the Ask a Spaceman and RealSpace podcasts, as well as the YouTube series Space In Your Face. As photons emitted by a star or galaxy spread through the Universe, the stretching of space causes them to lose energy. It's the space between us and those galaxies that is rapidly proliferating and stretching exponentially. Some sources suggest that the Big Bang caused an expansion that traveled faster than the speed of light. Space-time does not expand with respect to anything outside of itself, so the speed of light as a speed limit does not apply.
Because stretchy things are stretchy, objects close to you seem to move away at a certain speed, but objects farther away appear to move faster. You're asking a great question, the answer to which lies in the subtle difference between expansion that is faster than the speed of light and the propagation of information that is faster than the speed of light. The cosmological event horizon, on the other hand, defines a distance within which a future observer will be able to see the light, then ancient, that our small corner of space-time emits today. The expansion of the Universe is a growth of space-time itself; this spacetime can move faster than the speed of light relative to some other location, as long as the two locations cannot communicate with each other (or, in terms of rays of light, these two parts of the Universe cannot be seen together). The physics of that boundary is based, in part, on a part of the surrounding spacetime called the Hubble volume.