It's just for looks. (My under-cabinet hood came with an optional chimney.)

Thanks!

Any recommendations? I do want easily washable filters.

If you have an externally-vented hood (which you should with a 36" Wolf) there is going to be ductwork there one way or another. If it vents out the ceiling, you'll have a chimney -- it's a style thing whether you want an exposed chimney, or whether you want it covered with cabinetry.

Not necessarily, jakabedy. At our last house, we had a 30" vent hood that ducted behind the cabinet, up through the ceiling, and out the attic. Our handyguy used a flat rectangular duct and mounted the cabinet however many inches in front of it. It was awesome to have a full cabinet there, although the option to put the duct inside the cabinet (cutting out top, bottom, and shelves) is still preferable to me to a visible chimney. I also have modest kitchens, so I'd just really like the storage. Above-stove storage has always been my baking ingredient area and I'd hate to lose it.

We went with a chimney hood, given that our range sits between two windows and the hood had to stand on its own. However, one thing to think about is that most chimney hoods angle not just front to back as they go up, but also inward from the sides toward the central vent, thus reducing the capture volume and most probably also the effectiveness of the hood.

So how would something like the wall hood posted below work?

It would still need the vertical exhaust? Or could it exhaust horizontally to the outside?

Here is a link that might be useful: Wall Hood

Personal preference!

There are several types of filters...see the link below. It's a link to the Appliances Forum's FAQ on vent hoods.

Here is a link that might be useful: Applieances Forum - Overview of vent hoods

Many will vent either up or to the rear--you'll have to pull up the installation specs to be sure.