In this case I'm certain it's been done in post-processing: the background is too desaturated to look natural, regardless of the ambient light conditions. It's very easily done in post-processing: I've described a couple of techniques for Lightroom in this answer. They'll also explain how those touches of colour could have been left in the background while the rest is practically black and white.

You could get a result very close to this without post-processing though: it's all about white balance. The blowtorch is providing a very warm (i.e. yellowy/orangey) light source in the foreground. If the rest of the scene were lit by a cooler (bluer) light source (e.g. natural evening light) then you'd get something very similar to this if your white balance was set to target the foreground tones.

You can take the same principle even further by getting creative using remote-triggered flashguns and gels. Gels are just pieces of coloured plastic film that can be taped over the end of the flash to adjust its colour temperature (or change its hue completely). If you imagine a scene like this, but without the blowtorch providing a naturally warm light source, you could use an orange-gelled flash on your subject and blue-gelled flashes on the background to produce a very similar look.

Again, though, the background would be slightly blueish and would need some work in post-processing to completely desaturate it as above. However, for my money a more natural, cooler tone in the background would improve the shot considerably: too harsh a difference between saturated and desaturated areas always makes a shot look obviously artificial.

In this case I'm certain it's been done in post-processing: the background is too desaturated to look natural, regardless of the ambient light conditions. It's very easily done in post-processing: I've described a couple of techniques for Lightroom in this answer. They'll also explain how those touches of colour could have been left in the background while the rest is practically black and white.

You could get a result very close to this without post-processing though: it's all about white balance. The blowtorch is providing a very warm (i.e. yellowy/orangey) light source in the foreground. If the rest of the scene were lit by a cooler (bluer) light source (e.g. natural evening light) then you'd get something very similar to this if your white balance was set to target the foreground tones.

You can take the same principle even further by getting creative using remote-triggered flashguns and gels. Gels are just pieces of coloured plastic film that can be taped over the end of the flash to adjust its colour temperature (or change its hue completely). If you imagine a scene like this, but without the blowtorch providing a naturally warm light source, you could use an orange-gelled flash on your subject and blue-gelled flashes on the background to produce a very similar look.

Again, though, the background would be slightly blueish and would need some work in post-processing to completely desaturate it as above. However, for my money a more natural, cooler tone in the background would improve the shot considerably: too harsh a difference between saturated and desaturated areas always makes a shot look obviously artificial.