I was familiar with a line back in the early '80's popularized by Lev Alburt. I will attempt to assess the developments since then in this post.
1 d4 Nf6 2 c4 c5 3 d5 b5!?
The so-called Benko Gambit, originally called the Volga Gambit but Benko put his stamp on it in the early '70's. I will follow a particular line, but there are many opportunities for either side to vary along the way.
4 cxb5 a6 5 e3
Not played against me all that often, but since I prefer this move as White I will follow this line. A popular way to decline the gambit is 5 b6, which Sammy Reshevsky played when he was first faced with the gambit. In my internet play I have often faced 5 b3, which isn't even in the opening books! I guess the "book" feels 5 b3 is too passive, renouncing any hope by White of an opening advantage.
The system with 5 e3 was developed during the '70's and for a time was thought to be the refutation of the Benko. However, Lev Alburt developed an approach for Black which he unveiled against Benjamin at the 1984 United States championship, and which he wrote up in Chess Life under the headline "The Benko Still Lives". We will follow that line.
Alburt's original scheme had Black playing 5...Bb7, but I prefer the immediate capture.
6 Bxb5 Bb7
Threatening the White Pawn on d5.
7 Nc3 Qa5
Again the d5 Pawn is threatened.
Indirectly protects the d5 Pawn.
The Queen has done her duty by luring the White Queen Bishop to a useless spot on d2, where it blocks the white Queen from guarding d5. Now the Queen retreats, and the P/d5 is again threatened!
Not 9 Bc4 e6! 10 e4 Nxe4! 11 Nxe4 exd5 forking White's pieces.
The cornerstone of Alburt's system, which he called the "Barclay Gallery Variation after the friends who helped him develop it. White cannot take the Pawn because the Black Bishop takes on g2 and then takes the Rook on h1. Thus, the Pawn on d5 is again threatened.
10 Bc4 QxQ 11 BxQ Na6 12 Nf3 is comfortable for Black.
10...Nxe4 11 Nxe4 12 Qd3 f5 13 Ng3
Benjamin played 13 Ng5, but later analysis settled on this move as best.
Bxg2 14 Nle2
The original analysis from the '80's went 14 a4 Qb7 15 f3 Be7 16 N1e2 Bxh1 17 Nxh1 0-0 18 0-0-0 Nc6! 19 f4! However, a search of a 1991-present database showed only one game with 14 a4. That game, Vleijri-Vandenbussche (1994 corr.), continued 14...Nc6 15 BxN QxB 16 f3 BxR 17 NxB Rxa4 18 RxR QxR and 0-1 in 35 moves.
The preferred move today seems to be 14 N1e2, played 4 times to twice for 14 Nf3 and the one time for 14 a4. Hence I am giving 14 N1e2 as the new main line here.
14...BxR 15 NxB Be7
Played twice, to twice also for 15...Nc6. However, Be7 seems preferable, as Black need not worry about the Pawn on d7, as it is poison for White to capture it.
Getting the Knight out of the corner and back into the game seems best. White's plan in Groenewold-Wortel (1999) proved too ambitious. That game continued: 16. Bc3 O-O 17. Bxd7 Rd8 18. Qg3 Bf8 19. Bxe6+ Qxe6 20. Qg5 Qd5 21. Nhg3 Rxa2 22. Rc1 h6 23. Qxf5 Qxf5 24. Nxf5 Nc6 25. Rd1 Rxd1+ 26. Kxd1 Ra1+ 27. Nc1 Ra4 28. Nd3 g6 29. Ne3 Rh4 30. Ne5 Nxe5
31. Bxe5 Bg7 32. Bg3 Rb4 33. Nc2 Rxb2 34. Bd6 Bd4 35. f3 Kf7 36. Kd2 Ke6 37. Bf8 h5 38. Kd3 Kd5 39. Bh6 Rb3+ 40. Ke2 Kc4 41. Bd2 Rb2 42. Kd1 Kb3 43. Na1+ Kc4 44. Nc2 Ra2 0-1.
16...0-0 17 a4 Nc6 18 Bc3 d5
And now the game Sapi-Bliumberg (1994) continued 19. Qe3 Nd8 20. Nh5 d4 21. Nxd4 cxd4 22. Bxd4 Bb4+ 23. Ke2 Qc7 24. Bxg7 Qc2+ 25. Kf1 Qe4 26. Qxe4 fxe4 27. Bxf8 Kxf8 28. Nf6 Nf7 29. Nxe4 Ke7 30. Rc1 Ra7 31. Rc4 Ba5 32. b4 Bc7 33. Nc5 h6 34. h3 Nd6 35. Rg4 Kf6 36. Bd3 Nf5
37. Re4 e5 38. Rg4 Ne7 39. a5 Kf7 40. Re4 Bd6 41. a6 Kg7 42. Rc4 Kf7 43. b5 Nd5 44. Nb7 Be7
45. Rc6 Nf6 46. Bc4+ Kg7 47. Rc8 1-0