What are some common tactics or ideas that arise when black has played h6 (or white has played h3) in front of his castled king?
An example I have in mind is, in this position, white can win a pawn with Bxh6, gxh6, Qxf6:
A less concrete but still important idea is, with a bishop on the a2-g8 diagonal (pinning black's pawn on f7), white often plans to sink his king's knight into g6 in a couple of moves: