Tactics
The double check
Two pieces give check at the same time, which only a discovery can do. Blocking is impossible, because no square blocks both lines, and capturing is impossible, because no piece takes both checkers. The king has to move, every time, and that is what makes the double check the sharpest forcing move in chess.
How to spot it
Look for a discovered check where the piece stepping aside can also give check itself. Material is close to irrelevant here: a double check that drives the king onto a square where you mate is worth a queen, and most famous combinations end with exactly that trade.
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
12.Bb5+ Kd8 13.Re8#
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2. White to play Play it out →Answer
20.Rh5+ Kg8 21.Rh8#
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3. Black to play Play it out →Answer
20...Nxf1+ 21.Kg1 Qh2#
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4. Black to play Play it out →Answer
25...b2+ 26.Ka2 b1=Q#
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5. Black to play Play it out →Answer
32...Nf2+ 33.Kh2 Bb8+ 34.Nf4 Bxf4+ 35.g3 Ng4+ 36.Kh1 Rh2#
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6. Black to play Play it out →Answer
19...Nxd4 20.Rxc8 Nxe2+ 21.Kh1 Rxc8
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7. White to play Play it out →Answer
20.dxe7+ Kxe7 21.Re1+
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8. White to play Play it out →Answer
53.Nf8+ Kh8 54.Ng6+ Kh7 55.Rh8#
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9. White to play Play it out →Answer
34.Ne6+ Ke8 35.Nxc7+ Kd7 36.Nxd5
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10. Black to play Play it out →Answer
26...Ne2+ 27.Kh1 Qg1+ 28.Rxg1 Nf2#
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11. White to play Play it out →Answer
21.Qd8+ Kxd8 22.Nc6+ Ke8 23.Rd8#
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12. Black to play Play it out →Answer
23...Nxf3+ 24.Kh1 Qg1+ 25.Rxg1 Nf2#
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.