Earlier quoted context omitted.
Fares and rules come from ATPCO ( http://atpco.net ). Flights come from OAG ( http://www.oag.com ). Seat availability requires data directly from the carrier, usually via a live query to the carrier's reservation system. The GDS companies get this data from these sources and then in turn provide (crappy) APIs for customers to use to query it. In general, if you're doing bookings you can get small amounts of the data…
Thank you for building ITA Matrix - it is amazing tool and I don't know what I would do without it.
Honest question (I swear I'm not trying to troll): what do you actually do with it that you can't do (or do as well as) with Google Flights or Kayak or some other site like that?
I ask because I've used ITA Matrix and never managed to find a cheaper flight than I can through "normal" means... but I rarely fly multi-destination (and basically never do more complicated stuff) so I'm not sure if the use case is beyond mine or if I just don't know how to utilize it in a useful manner.