The position in the Ruy Lopez after 9. h3 is one of the most strategically interesting in the whole of opening theory. Blacks reasonable options at this point run to double figures, which for a position nine moves into the game is almost unique.
9...Na5 is the old main line, the Chigorin Variation. Black hunts down Whites light-squared bishop and frees her c-pawn. The knight may end up back on c6, on c5 via b7, or on c4, depending on developments elsewhere.
9...Nb8, the Breyer Variation, is the other traditional move. With White taking her time developing her queenside, Black reckons she can spare two moves to redeploy the knight on d7 out of the way of the bishop which will appear on b7. It is a little more committal than the Chigorin and appeals to defensive-minded players.
9...Bb7, the Zaitsev, is the current red-hot theoretical battleground. The bishop eyes up the e4 pawn and the knight reserves its options.
9...h6 is the Smyslov Variation. The Zaitsev is considered an improvement on the Smyslov; in the Smyslov the bishop will usually go to b7, but in the Zaitsev Black can usually manage without ...h6.
9...Nd7 on the plus side enables an f5 advance and controls g5, and on the minus side clogs up the queenside and removes a defender from the king.
9...Be6 is another way to challenge the b3-bishop, usually leading to an exchange of bishops and a boring position in which White has a little more activity.
9...Re8 will transpose to the Zaitsev unless both players are desperate for a draw by repetition.
9...a5 is a quirky attempt to force matters on the queenside. White will probably meet it with a central charge.
9...Bd7 and 9...Qd7 are both at least semi-useful, and even 9...d5 doesn't lose on the spot - although players interested in getting their d-pawn to d5 should look at the Marshall Gambit on move 7.