White's sacrifice of a bishop on h7, sometimes known as the "Greek gift," can begin a common, important, and complex set of mating concepts. The elements of the mate generally involve three core pieces: a bishop, a knight, and a queen. The basic idea, starting from the diagram, goes 1. Bxh7+, KxB; 2. Ng5+, Kg8; 3. Qh5 and then 4. Qh7#, where the queen mates with support from the same knight that drove back the king on the second move. This is the ideal form; in practice the pattern can be complicated in several ways. On his second move Black can play his king to g6 or h6 instead of g8. Or Black may be able to capture the knight on g5. Or after White’s third move (Qh5) Black’s king may be able to scurry off along the back rank. Or Black may be able to decline the sacrifice in the first place, responding to Bxh7 with Kh8.
Then there also are some chances for variety on White’s side: instead of Ng5 he can follow up on the bishop sacrifice with Qh5 right away or some other action on the h-file. The result of all this may be mate, or it may be a gain of material the enemy sacrifices to avoid mate. Or it may just be the pawn on h7 when your opponent declines the sacrifice.
As this description suggests, the mating ideas we will consider here differ from those we have seen before; they tend to involve more different issues to worry about, and can become quite involved. To catalogue all these variations, and the variations within them, would take too much space for our modest purposes, so in this section (and two more that follow) we will just look at the basic ideas behind them. The pattern arises often, so familiarity with its key ideas is useful.