no need for analysis... you are winning in material with stronger pawn structure, his attack has been stalled by your proper defense. nice!

Yes, White should definitely win this position. Black pretty much has to move his bishop, after which you (probably) get a choice of which pawn to take, unless Bd3, in which case you can take Qxd5+. He could harass your rook, but apart from that, Black's position looks to be going downhill from here.

20... Qe2+!
21.kg1 leads to draw by repetition, or 22. Rf2 pin followed by Qe1+ Qe3+ same story. The rook will have to move.
21. Rg1 leads to draw by some sacs and strong play from black (rxe5 dxe5, Bxf3 gxf3, Qxf3+ draw by repetition.
so b,d,e,f,g,h are bad or impossible for the rook, only possibilities are a (bad but maybe best) and c, possibly back to Qe3, back to f, or a.
so eventually rook to a.
With rook on a, I'd try to draw by: rxe5 dxe5, Bxf3 gxf3, Qxf3+ with possibilities.
The win is far from granted

21 ....Qe2   22 Rg1  Rxe5   23 dxe5 Bxf3   24 Qc8+! Kf7   25 Qf5+ and wins.

good ideas Bastiaan, but no cigar, this time.

As I said earlier, the position is anything but simple. Let me demonstrate:

Black has 20... Rf8, 20... Qf4 ; in none of these can white can immediately capture the bishop as his rook is endangered and mate is threatened. He can play 21. Rg1 after which he can seriously threat to capture the bishop. The same goes against 20...Qe2.

 On the other hand, black cannot withdraw his bishop right now anywhere (except 20... Bxf3 and 20... Bf5) because of 21. Qxd5+ Kh8 22. Nf7+ Kg8 23. Nh6+  Kh8 24. Qg8+!! Rxg8 25. Nf7#!

20... Bxf3 21. gxf3 open to further analysis (white still threatens Qxd5+)

20... Bf5 21. Qxd5+ Be6 22. Qc6 open to further analysis.

20... Rxe5? loses because of 21.Qc8+ Kf7 22. fxe4+! and black is a piece down.

Bastiaan and Ray_Brooks, thanks for your posting.

After 20... Qe2 21.Rg1 Rxe5?! 22. dxe5 Bxf3? will not work - thanks Ray_Brooks for pointing that out.

20... Qe2 21. Rg1 Rxe5?! 22. Qc8+ Kf7 23. dxe5 Bd3 (or Bc2 or Bg6? otherwise bishop goes without compensation) 23.Qxc7+ and I think white is much better off! 

 Right, I didn't see that. thanks