I would like to have some analysis in the following setting:
1. e4 Nf6 2. e5 Nd5.
Now, what is best for white? The move
3. c4 continues the attack, but can create a "pawn weakness".
1.e4 Nf6 is called Alekhine Defence. It's an hypermodern opening as it doesn't directly fight for the center but more aim to provoke weakness in White camp and then counter-attack.
Also White has several option, first he can try not to push by playing : 2.Nc3 2.Bc4 as after 2...Nxe4 White get back the pawn with 3.Bxf7 Kxf7 4.Qh5+ g6 5.Qd5+
Still, it's better to take the center : 2.e5 Nd5 and now White has to decide whether or not he will push his pawns, so 3 systems are relevant :
the modern approach, White delays c4 : 3.d4 d6 4.Nf3 just finishing his development without giving weakness
3.d4 d6 4.c4 Nb6 5.exd6 and now Black has a choice between ...exd6 or ...cxd6 depends where he wants to put his bishop f8.
the most agressiv : 3.d4 d6 4.c4 Nb6 5.f4 just taking as much space as possible, I think this is the most critical continuation.
Read up on The Alekhine Defense. It's a Hypermodern opening wherein Black purposefully allows his King's knight to be harassed by pawns. The intent of this is for Black to allow White to induce weaknesses in his pawn structure which eventually collapses. On the other hand, if White can keep it together, he retains a tremendous amount of space in which to develop an attack.
Here's an example where Shabalov beats Nakamura with this defense.
[Result "0-1"] [White "Nakamura, Hikaru (2658)"] [Black "Shabalov, Alexander (2606)"] [Event "USA-ch"] [Site "Stillwater"] [Date "05/18/2007"] [Round "4"] [FEN ""] 1. e4 Nf6 2. e5 Nd5 3. c4 Nb6 4. d4 d6 5. exd6 cxd6 6. Be3 g6 7. d5 Bg7 8. Bd4 Bxd4 9. Qxd4 O-O 10. h4 e5 11. Qd2 f5 12. Nf3 Qf6 13. Nc3 Na6 14. Qh6 Qg7 15. Qd2 h6 16. Nb5 Rf6 17. Qa5 Nd7 18. Qa3 Qe7 19. Be2 e4 20. Nd2 Ne5 21. O-O-O Nc5 22. Kb1 Ncd3 23. Bxd3 Nxd3 24. Rhf1 Bd7 25. Nd4 Qe5 26. Qc3 b5 27. cxb5 Rf7 28. f3 Rc8 29. Nc4 Qxd5 30. fxe4 Qxc4 31. Qxd3 Qxd3+ 32. Rxd3 fxe4 33. Rxf7 exd3 34. Rf1 Rc4 35. Nc6 d2 36. Ne7+ Kg7 37. Rd1 Kf7 38. b3 Rc1+ 0-1