In the game Carlsen-Anand (Norway 2013) they got very soon following pawn structure:
As you easily can see it is a better one for white. Black has an backward pawn on d6 and white has the option to build an outside passer.
In the game we see that Carlsen played very classical. He stopped the advance of the d-pawn and and tried to hold down the Black initiative on queen side, carefully reducing the material by exchanges.
So, after 25. Kf1 White had an advantage of ca. 0.70, if you want to believe Houdini 3. The pawn structure was almost the same (backward pawn and option of an outside passer) and reduced material. But Anand managed to hold the c-file with a rook and to exchange his bad bishop against the better one of Carlsen. Finally he managed even the advance of his backward pawn
This game may have shown that the "weakness" of a backward pawn is not enough for a win, even if the White strategy is successfully and the Backward pawn becomes blockaded and the material reduced by exchanges.