From the AIM in the US...
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5-5-15. Minimum Fuel Advisory
a. Pilot.
1. Advise ATC of your minimum fuel status when your fuel supply has reached a state where, upon reaching destination, you cannot accept any undue delay.
2. Be aware this is not an emergency situation, but merely an advisory that indicates an emergency situation is possible should any undue delay occur.
3. On initial contact the term "minimum fuel" should be used after stating call sign.
EXAMPLE-
Salt Lake Approach, United 621, "minimum fuel."
4. Be aware a minimum fuel advisory does not imply a need for traffic priority.
5. If the remaining usable fuel supply suggests the need for traffic priority to ensure a safe landing, you should declare an emergency due to low fuel and report fuel remaining in minutes.
REFERENCE-
Pilot/Controller Glossary Item- Fuel Remaining.
b. Controller.
1. When an aircraft declares a state of minimum fuel, relay this information to the facility to whom control jurisdiction is transferred.
2. Be alert for any occurrence which might delay the aircraft.
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this means when your fuel state indicates you will land with less than planned min fuel, you advise ATC. It does not mean special handling or an emergency but does mean you can't take a lot of delays or holding. It also does not mean you have to divert.