It depends on the airline.
Some airlines use enlarged crews for all flights longer than ~10 hrs.
That means that there are three pilots on board, 1 captain, 1 senior first officer and one first officer, or 2 captains and 1 FO. The relief pilot has a crew rest compartement behin the cockpit.
That airlines also have an enlarged cabin crew, with crew rest compartements under the floor.
I know that for example Austrian is an airline that has enlarged crews on their long haul flights (e.g. to japan, south africa), as well as Lufthansa and a lot of other airlines.
But there are airlines, that NEVER use enlarged crews, regardless the lenght of the flight.
Mainly charter airlines have this poilicy. There are airlines arround where pilots have a maximum allowed flying time of 18hrs (!) in a 2 Man Cockpit. They really need a lot of coffee.....But the passengers don´t realize that, and no newspaper write about it, so the management dosn´t care about it. These airlines get prizes for their tasty food and their great service - that the pilots are tired and exhausted is of no interest for most of the people.