In short:
There are no ICAO locations beginning with X, as evidenced by the official list in Doc 7910.
ICAO location indicators are used to route messages between stations of the aeronautical fixed service (AFS), the service collectively provided by all ICAO members to facilitate international aviation.
Doc 7910 contains the list of all international location indicators, and each State also includes the indicators it manages in its AIP, at section GEN 2.4 (example).
Note ICAO 4-letter indicators are not always associated with a particular aerodrome, e.g. France uses the common address LFZZ to receive and transmit NOTAMs.
Location indicators are AFTN locations.
Civil aviation entities across the world rely on the aeronautical fixed service (AFS) for the exchange of messages and data to coordinate international civil air traffic. They are connected by the aeronautical fixed telecommunication network (AFTN), a kind of teletype network.
Each entity participating to the AFS receives a 4-letter location indicator for message routing through the AFTN. Large aerodromes, potentially involved in international traffic are part of the AFS, Aerodromes not involved in the AFS are not connected to the AFTN, they don't need an ICAO indicator.
The 4-letter indicator is then suffixed to get unique addresses for all services (tower, weather services, control center, air authorities...).
Routing scheme
The first letter of a location indicator delimits routing regions:
(From Doc 7910)
Within a region, a second letter is used to create blocks allocated to States and Territories. Many States need blocks in different routing areas (e.g. France uses blocks LF-Metropolitan France, TF-Antilles, SO-Guiana, FA-Polynesia and a few other).
The third letter is a communication center used by a group of stations, and the fourth letter is the station.
Blocks are allocated by ICAO, the last two characters of the location indicator are determined by the State/Territory to which the block has been allocated.
Three more letters are added to the location identifier (according to Doc 8585 - Designators for Aircraft Operating Agencies, Aeronautical Authorities and Service) to reach a particular service. For examples:
- YXY to reach a military organization
- ZTZ to reach the control tower
- ZZZ to reach an airborne aircraft
A message sent to EBLGZTZX is sent to EBLG = Liège Airport, ZTZ = control tower. X is a filler character for a fixed length of 8 characters.
Indicators vs. Aerodromes
A 4-letter location doesn't necessarily designate an aerodrome, e.g., these locations are not associated to a particular aerodrome: LFFF (Paris UAC control), LFYX (Air Force Paris area), LFZZ (France NOTAM management).
Many aerodromes have no ICAO location indicator, because they are not involved in international operations.
Some location indicators correspond to AFTN unconnected stations.
No X area
There is no routing X area, and as a matter of fact:
- The last W block allocated by ICAO is WS, to Singapore.
- The next block is YA, allocated to Australia.
Often cited, XBRO is not an ICAO indicator for Broadford_Airfield. However many databases include(d) it, e.g. OurAirports (note the code in the URL), and flight simulators have reused it, this creates problems.
Any organization can create 4-letter identifiers, and identifiers starting with X can exist. But they have no link with AFS/AFTN, they don't represent known ICAO locations.
I don't know why X was excluded as an area (contrary to I and Q for obvious reasons). Perhaps this is linked to the fact X is used as a filler, or could be used to strikeout a whole location designator.