You might be able to tell from the title that I didn’t really know what to call this effect but I think it’s pretty nice on the right photo and it’s ultra-quick.
Here’s our starting photo by The Pug Father.

by The Pug Father

All you have to do is make a duplicate of the Background layer (Ctrl+J) and set its Blend mode to Soft Light then just select the Background layer and desaturate it (Ctrl+Shift+U) and you’ll get a nice contrasty image with muted colours like this…

grunge-mute-2

As a special bonus, if you now select the Soft Light layer (Layer 1) again and duplicate that (Ctrl+J) you’ll bring back more of the colours from the original image but still have a really nice grungy image like this…

grunge-mute-3

I think that looks pretty good! For extra grunge you might want to combine this effect with a grungy texture overlay.