Our last immortal mates were Damiano's and the dovetail mate. Think you can spot them in the following positions? (White to move, solution at the end.)
Strictly speaking, the dovetail mate is not an immortal mate; after all, it doesn't commemorate any particular chess player. Two other such mates are the epaulette mate and the guéridon mate. Back in the days when the French were a force to be reckoned with in the chess world (no offence, Monsieur Bacrot), people sometimes named mates after things from France. Epaulettes are shoulder ornaments that used to decorate French army uniforms; in the epaulette mate, the mated king cannot escape because it is sandwiched between two friendly pieces.
In the guéridon mate, two pieces to the left and right behind the king prevent it from escaping on the diagonal; the setup resembles a guéridon, a peculiarly shaped French coffee table.
Returning now to a true immortal mate: Gioachino Greco was a 17th century chess master whose legacy lives on in Greco's mate, a file/rank mate delivered by a queen and a bishop:
(Solution to the quiz: (a) 1. Qxd6+ Kxf7 2. Rf1+ Kg7 3. Qf6# leads to a dovetail mate; (b) 1. Rf8+ Bxf8 2. Qf7+ paves the way for Damiano's mate.)