Checkmate patterns
Pillsbury's mate
A rook comes down to the back rank or across the g-file to mate, and a bishop on the long diagonal stops the king stepping away. The bishop does not give the check, which is what makes the pattern hard to see: the piece doing the important work never touches the king.
How to spot it
Whenever you have a bishop on the long diagonal aimed at a castled king, count what mates if a rook lands on g1 or g8. The pawn on g7 or g2 is usually the only thing in the way, and removing it, with anything, is often the whole combination.
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. White to play Play it out →Answer
21.Qxf8+ Kxf8 22.Rd8#
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2. White to play Play it out →Answer
28.Qxf8+ Kxf8 29.Rc8+ Bd8 30.Rxd8#
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3. White to play Play it out →Answer
28.Qxh7+ Kxh7 29.Rh5#
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4. White to play Play it out →Answer
30.Qd8+ Rxd8 31.Rxd8#
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5. Black to play Play it out →Answer
25...Qxf1+ 26.Kxf1 Rb1#
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6. White to play Play it out →Answer
21.Bg7+ Kg8 22.Bxe5#
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7. Black to play Play it out →Answer
30...Bf1+ 31.Kh1 Bh3#
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8. White to play Play it out →Answer
28.Rg7+ Kh5 29.Be2+ Kh4 30.Bg3+ Kh3 31.Rh7#
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9. Black to play Play it out →Answer
31...Rxg2+ 32.Kh1 Rg1+ 33.Kxg1 Rg8+ 34.Bg5 Rxg5#
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10. White to play Play it out →Answer
19.Bf8+ Bxh5 20.Rxh5#
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11. White to play Play it out →Answer
17.Rxg7+ Kh8 18.Rg8+ Kxg8 19.Rg1#
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12. White to play Play it out →Answer
22.Rh3+ Kg8 23.Ne7+ Kf8 24.Nxg6+ Ke8 25.Rh8#
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.