Win or draw?

I see a win there, how about checking this out?

http://www.mychessblog.com/endgame-technique-king-and-queen-against-pawn-on-7th-rank-with-support-of-king/ 

Bring you king over, job done

59... Kc7 was the move that drew the game. Once the white king can reach h8 you can't take the pawn as it becomes stalemate. 59... Qh8+ wins.

Thanks everyone, I will keep this in mind next time such thing happens ;)

Frankdawg 2. Kd6 and Qc8 is easier; Kd8 is the right "defense" for longest
Also Timnhan is correct :D

However, THIS is draw

Godspawn has got it, but there is more than one way to win. As long as you remember to stop the black king from connecting with the pawn, whilst keeping it from promoting and bringing your king up for the attack. This is done through checking!

That is indeed very effective as well, however in this situation there is more than one way to skin a cat I'm just showing the way I would do it.

okay maybe Kd6 lasts a bit longer due to that nice little tactic posted above ^.^

This is King/Queen vs King/7th-rank pawn endgame theory. It happens quite often after pawn races. You should at least know what's winning and what's drawing even if you don't know exactly how. It is somewhat complicated but not overly difficult to learn.

In a nutshell, this ending can be broken down into three parts:
1. 7th-rank king-, queen-, and knight-pawns are easy wins for the stronger side.
2. 7th-rank rook-pawn is only a win if the stronger king is in the 'winning zone', two moves from key-squares g6 and f7 (in the case of rook-pawn on h7).
3. 7th-rank bishop-pawn is less straightforward. There are two 'winning zones', depending on whether the weaker king is on the exposed side of the bishop-pawn (the case here) or the protected side. On the exposed side the winning zone is two moves from key-squares g6 or d7 (for bishop-pawn on f7). On the protected side the winning zone is only one move from key-squares g6 or e7, which is a significant reduction in the winning zone compared to the exposed side.

From this we can deduce the strategy for each side in the position shown in the original post: the weaker side should, of course, queen the pawn if given the opportunity before the stronger king makes it to the key squares; but failing that, get to the protected side in order to reduce the size of the 'winning zone' and access the h8-stalemate motif. The stronger side should, ideally, get in front of the pawn with the queen (auto-win); but failing that, occupy the protected side with the queen while preventing the pawn from queening. As ReasonableDoubt showed, it's possible to do this with one move.

It's instructive to look at a failure by the stronger side:

(Note that this family of endgame theory is riddled with exceptions, tricks, and tactical motifs that can turn theoretical draws into wins, wins into draws, if you're not playing a computer.)

Here's another failure by Black (I think the OP has hit on one of the most instructive positions in this family of endgames).

Huh I dont understand the rook one, isnt that won at all times too? the rook pawn and king vs king and queen, I thought the stronger side should win it (of course maybe some exceptions, such as the king BLOCKING the queen or something, must be one somewhere)

No, there are stalemate themes for the 7th-rank rook-pawns just like the 7th-rank bishop-pawns (we are talking about a 7th-rank rook's pawn, not a 6th-, 5th-, 4th-, etc-rank rook's pawn).

61 Ke8 Kc7...an amusing possibility.