Tactics
En passant
A pawn that has just moved two squares can be captured as if it had moved one, by an enemy pawn beside it, and only on the very next move. It is the rule everybody learns and nobody remembers, and there are positions where it is the only move that works.
How to spot it
The right of capture expires immediately, so the moment an enemy pawn passes yours is the moment to look. The tactical version is not about winning the pawn: it is that the capture opens a file or a diagonal, and the thing at the end of that line is what you were actually playing for.
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
16...dxc3#
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2. Black to play Play it out →Answer
25...Ba6+ 26.Bb5 Bxb5+ 27.c4 bxc3#
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3. White to play Play it out →Answer
27.Be4+ f5 28.exf6#
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4. Black to play Play it out →Answer
48...Nd4+ 49.Nxd4 Kxd4 50.a4 bxa3
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5. White to play Play it out →Answer
32.Bh3+ f5 33.gxf6#
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6. White to play Play it out →Answer
42.a6 b5 43.cxb6
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7. Black to play Play it out →Answer
7...Qb6+ 8.d4 exd3+ 9.Nd4 Qxd4+ 10.Be3 Qxe3#
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8. White to play Play it out →Answer
10.Qb3+ d5 11.exd6+ Be6 12.Qxe6#
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9. White to play Play it out →Answer
38.f5+ Kh6 39.Be3+ g5 40.fxg6+ Kxg6 41.h5#
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10. White to play Play it out →Answer
24.f5+ Kh6 25.Bf4+ g5 26.fxg6+ Kxg6 27.h5#
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11. White to play Play it out →Answer
25.Rxh8+ Kg7 26.Bd4+ e5 27.dxe6+ f6 28.R1h7#
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12. White to play Play it out →Answer
11.h5+ Kh6 12.d4+ g5 13.hxg6+ Kxg6 14.Bd3+ Kg7 15.Bh6#
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.