Hinges, or joints, come in halves. Riveted joints are usually found on the nicer frames. We can re-pin these if they have come out or replace the pinned joint with a new one if it has broken entirely.
Alternatively you may have a heat sunk joint. These are inserted in the frame by the use of a piece of apparatus that is effectively a heated pair of tongs. The joint melts its way into the frame.
On the temple (arm), if it is not pinned then it most likely part of the wire that runs through the temple. Replacing that is troublesome. The best way to fix that is to have a new joint laser welded on.
Finally spring hinges as found on arms sometimes. If these break, a replacement will need to be laser welded on. There may be a little bit of evidence of this but it is not obvious when completed.