Checkmate patterns
Morphy's mate
A bishop mates a king in the corner while a rook takes away the escape square, the king's own pawn covering the rest. One of several patterns carrying Morphy's name, and the reason is the same in each case: he played them all first, against people who had not seen them.
How to spot it
The king in the corner with a pawn on g7 or g2, and a bishop of yours on the long diagonal. Then the rook only has to reach the file or rank beside the king, and clearing the diagonal is the sacrifice worth calculating.
The positions
Easiest first. Every one is from a real game, and the rating under each board is what it costs the players who have tried it on lichess.
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1. Black to play Play it out →Answer
32...Rg8+ 33.Kh1 Bxf3#
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2. White to play Play it out →Answer
17.Nf6+ Ke7 18.Bc5#
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3. Black to play Play it out →Answer
27...Rg6+ 28.Bg5 Rxg5+ 29.Kh1 Bxf3#
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4. White to play Play it out →Answer
34.Ba5+ Kd7 35.Nc5+ Ke7 36.Bd8#
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5. Black to play Play it out →Answer
32...Rf5+ 33.Kg4 h5+ 34.Kh4 Bf6#
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6. Black to play Play it out →Answer
32...Qf1+ 33.Kh2 Qg1+ 34.Kh3 Qh1+ 35.Kg3 Bf2#
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7. White to play Play it out →Answer
39.Rg7+ Kh6 40.Bg5#
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8. Black to play Play it out →Answer
23...Rxc3+ 24.bxc3 Ba3#
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9. White to play Play it out →Answer
23.Qxf7+ Kxf7 24.Bd5#
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10. Black to play Play it out →Answer
35...Qxh4+ 36.gxh4 Bg1+ 37.Kh3 Bg2#
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11. Black to play Play it out →Answer
31...Qf3+ 32.Bxf3 Bxf3#
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12. Black to play Play it out →Answer
26...Re1+ 27.Kg2 Rg1+ 28.Kh3 Be6+ 29.Bf5 Bxf5+ 30.g4 Bxg4#
Reading about a pattern is the easy half. Motify finds the positions where you missed one, by running your own lichess and Chess.com games through Stockfish, and puts each of them behind two or three puzzles on the same idea so you meet it having just found it three times. See how Motify works.
Positions from the lichess puzzle database, released under CC0.