Tactics
The exposed king
A king without pawns in front of it, or a king dragged into the middle of the board, is a target rather than a piece. Material stops mattering in these positions, and the right move is usually the one that brings one more piece to the attack rather than the one that wins a pawn.
How to spot it
Count the squares the king has and the defenders within reach of it. When they have fewer defenders nearby than you have attackers, there is something there, and the move to look for first is the check that takes a flight square away rather than the check that looks most violent.
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.
-
1. Black to play Play it out →Answer
33...Rf1+ 34.Ke2 R8f2+ 35.Kd3 Rd1#
-
2. Black to play Play it out →Answer
20...Ng4+ 21.Kxh3 Nxf2+ 22.Kg2 Nxd1
-
3. Black to play Play it out →Answer
34...Qf2+ 35.Kh3 Rf3+ 36.Qxf3 Qxf3+
-
4. White to play Play it out →Answer
12.Bxd7+ Nxd7 13.Qh5+ Bg6 14.Nxg6 hxg6 15.Qxh8
-
5. Black to play Play it out →Answer
30...Rxh2 31.Qxh2 Nxf3+ 32.Kc2 Nxh2
-
6. Black to play Play it out →Answer
61...g4+ 62.Kf2 Kh2 63.c5 g3+ 64.Ke2 g2
-
7. Black to play Play it out →Answer
29...Be3+ 30.Kh1 Qxh3+ 31.Rh2 Qxf3+ 32.Qxf3 Rxf3
-
8. Black to play Play it out →Answer
44...Ne4+ 45.Kxb3 Nd2+ 46.Kc2 Nxf1
-
9. White to play Play it out →Answer
39.f7+ Kxf7 40.Ne5+ Kg7 41.Nxc4
-
10. White to play Play it out →Answer
21.Rg3+ Kf7 22.Rg7+ Ke8 23.Rxe7+ Kxe7 24.Bxf6+ Rxf6 25.Qxh5
-
11. White to play Play it out →Answer
20.Bg5+ Rxg5 21.Qf8+ Kxc7 22.Qd6#
-
12. White to play Play it out →Answer
30.Qd8+ Kg7 31.Ne6+ Kh6 32.Qh4#
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.