I find this stuff really interesting, so if anyone's curious, here's a few more tidbits:
GPS system time is currently 18s ahead of UTC since it doesn't take UTC's leap seconds into account [0]
This (old) paper from USNO [1] goes into more detail about how GPS time is related to USNO's realization of UTC, as well as talking a bit about how TAI is determined (in hindsight! - by collecting data from clocks around the world and then processing it).