The Houthis in Yemen claimed responsibility, but the Saudis and the US government claim that it was an Iranian strike.
While it is highly likely that the Iranians have been providing the technical support to the Houthi drone effort, the provenance of the actual attacks is unclear.
What is clear is that the House of Saud is facing some well-deserved blow-back for their brutal war on the people of Yemen.
There is a claim that the Houthis lacked the ability to make a missile with the range for this task, but given that the Houthis literally had a static displays showing missiles with ranges up to 1700 km 2½ months ago, which would suggest that these capabilities are nowhere near as difficult to acquire as has been implied.
The question here is guidance, and why I call this a missile rather than a drone; the 1250 km range puts the vehicle well out of the range of the control of a base statement without a satellite link, which the Houthis do not possess.
The attacks are very precise.
In fact, the precision seems to exceed the what one could get with GPS, which could not be any less than the 15 meter range.
It is possible that they get less error by using a D-GPS installation, which could increase the accuracy to less than 1m, but the nearest installation (Al-Ahsa International Airport) would be about 80 km away, and you would need a relatively sophisticated inertial guidance to preserve that position information.
Similarly, the use of Terrain Contour Matching (TERCOM) might work, but again this would seem to exceed the capabilities of the Houthis.
Given that the Russian KH-5, that the Iranian Soumar is derived from has a CEP of 25m, this implies some sort of terminal guidance.
The two alternatives here are some sort of image based targeting, either TV of IR, or the use of a laser designator on the ground.
Given that the area around both Abqaiq and Khuaru are majority Shia (See map, blue is Shia, red is Sunni, yellow is Wahhabi), I think that there is a very real possibility that there was someone on the ground designating the targets.
As an aside, it should be noted that these attacks indicate a serious shortcoming of the US Patriot SAM system as compared to the Russian S-300 and S-400.
First, the Patriot has about a 90 degree coverage as compared to the full 360 degree coverage given by the Russian systems.
It should be noted that the MEADS missile system would have resolved this issue.
Secondly, the Russian systems are designed to use quick erecting elevated radar masts which are more likely to detect low flying cruise missiles.
Certainly, the Russians are using this event to sell their systems.