Fight for the center
The variation with 9.Nh4 has its own flawor. For the other main lines, the logical plans flow from the strategic evaluation of each side's plusses and minuses:
- White enjoys the better center. Black's dxc4 was a slight concession in the fight for the center, Pd4 is firmly established.
- On the other hand, Black has freed both his bishops, while White's queen bishop is still locked inside his pawn chain.
- White has a very slight development advantage, having already castled.
- White's Q-side is slightly weakened by the a2-a4 advance. The stronghold on b4 for one of Black's pieces makes his lack of space more manageable.
As a consequence, White aims to increase his space adantage, free his Bc1 and set his center in motion with e3-e4. If possible, he would also like to provoque weaknesses in Black position (the usual suspects are Pb7 fixed by a4-a5 or targeted by Qb3, and the kingside pawns White tries to induce into advancing by threatening a K-side attack, or wants to double with an exchange on g6).
Conversely, Black tries to slow down White advance on e4 (8...0-0 9.Qe2 Bg6!?, e.g., aims to avoid 10.e4 Bxc3 11.exf5), complete his development, and nullify White's central advantage by exchanging the Pd4 with ...c6-c5 or ...e6-e5 (Nbd7, Qe7/Qa5,Rc8/d8/e8 are typical preparatory moves to engineer those breaks). Alternatively, he can put pressure on White's e4-d4 center when it's formed in order to provoque an early e4-e5 (which gives White attacking chances on the K-side but also the d5-square for Black).
The battle for and against e4 is the main topic of the next 5-10 moves.
You can check several battles from the Topalov-Kramnik Elista WC match (WC stands for 'World Championship', not for 'Toiletgate'), or old games by Max Euwe and Gideon Stahlberg.