That down there is a DPF on a Volvo C30. Here beginneth a thread on how to replace it.

First, you need to clear some pipework out of the way. This includes the intercooler charge pipe, which is mounted to the side of the gearbox.

Remove the heat shields, and you will have access to the clamp that mounts the DPF to the turbo. Loosen it. Then remove the fasteners from the other mounting points.

Unless you have a pair of strong forceps (or the strength of Thor), you'll never pull this clamp apart far enough to get it off. I thread two nuts in between, and while holding one, crank the other up the bolt. It's slow, but works to open the clamp up enough.

With everything loose, remove the pressure hoses and the temperature sensor from the sides of the DPF.

Then simply slide the DPF out from the bottom. It will take a bit of persuasion, and you need to be careful not to snag the lower coolant hose. But with patience, it's easy enough to do. I find keeping the heat shield on is much easier than trying to remove that first.

What causes a DPF failure is an accumulation of ash. You can determine that with a reading from the software, or a pressure test. Here's a very unscientific test, though: The new DPF weighs nearly 2kg *less* than the old one.

(Yes, that's the kitchen scale. Don't tell my wife.)

You'll need to remove the lower pressure line to fit to the new DPF. It's been exposed to exhaust heat, so use lots of penetrating fluid (or heat), and take your time.

Install the pressure line and the heat shields, and you are ready to begin reassembly.

Push the new DPF up through the bottom. Once it's about 3/4 of the way up, I like to come on top and pull it the rest of the way. Easier to wiggle into place. Loosely fasten the turbo clamp first so it doesn't fall on you later. Also makes it easier to line everything up.

And that's it. I'll need to wiggle it round a bit to get it refastened properly, but then just reattach the hoses and temp sensor, and put all the plumbing back in place. I'm also going to top off the additive fluid, but that will be for another day.