Product review (5 stars): this was perfect for my needs!
I never had a stove without a range hood, but when I moved in my new house (which is actually a very old house) there were only cabinets above the stove. No hood at all. I really missed the light the most! Venting would have been very difficult as the house is made of stones, and the walls inside are concrete blocks with metal mesh holding plaster. Not a simple drywall type installation at all. So I decided a ventless hood was the best and easiest option for me. I worried that it wouldn't be effective, but it does a surprisingly good job at moving air. A little noisy, but most hoods I have ever owned were slightly noisy. There is a clip-on cover for the front little vents if you indeed have a vented option.

I did not know that hood was not shipped with the extra filter needed for ventless operation. There is a mesh cover for the fan, but it is not a filter. Further, the item amazon featured on the hood product page was NOT the one that went with this. I went to the Braun website and still was confused. I finally found the right one: it is this one:<a data-hook="product-link-linked" class="a-link-normal" href="/Broan-41F-Range-Hood-Filter/dp/B000VL060M/ref=cm_cr_arp_d_rvw_txt?ie=UTF8">Broan #41F Range Hood Filter.</a>&nbsp;There may be non-Broan brand filters available, but I wanted to be sure I got the right one, so I went with the name brand the first time. This filter is installed with the blue side next to the blade and then put the included mesh screen over that. There is a clip that holds them in place.

The hood does require hard wiring. I did not have that either!! (Why are these projects always so complicated?!!!) However, there is an item available (and noted on the Broan website) called BR-HCK44 - Range Hood Power Cord Kit.  It is "for use when hard wiring is not an option and a plug is needed." There is also a wall mounting bracket (BR-35) for installations where there is no upper cabinetry. I didn't need the bracket as I had upper cabinetry. I don't think either are available here on amazon, but just google the model number/name and you will find one. They are relatively inexpensive.

I actually had to run my new plug cord down the wall and use the outlet behind the gas stove. If you have a similar problem, here is my solution, maybe it could work for you, too. I was putting in a glass tile backsplash behind the stove anyway, and wanted wood or ceramic border to "frame" the small tiles. I figured I could use the recess of one of the trim pieces to hide the cord as it ran down the wall and then simply plug it into my grounded outlet behind my gas stove. (Most gas stoves need an outlet behind them for clocks, electric ignition, timers, oven light, etc.) I couldn't find any ceramic that worked, but instead routed out some trim molding with a dremel, tucked the cord behind that channel, and used the wood to frame my tile backsplash. The wood should be safe, it is no closer than any adjacent cabinetry would be. You can't tell there is a cord there, and it is pretty protected from bumps since it is behind the molding. (I just used little finish nails in case I need access to it in the future. I put them in the wood first so I wouldn't nick the cord.) I did need a short grounded extension, too...the add-on cord was only 3 feet long, but the ugly stuff is behind the stove. It was a tricky problem, and some of you may already have wiring in place, but just in case you run into something like I did, I thought I would post my work-around! Maybe I will post a picture of it one of these days!

One more tip...if you have to install this by yourself (like I did) it is HARD holding the thing up with one hand (and your head!) and marking the holes for drill/screws with the other! SAVE your packing box, put it on your stove and put the hood on top. It will hold your hood very close to its final position for you so you can make the marks for the screws! I think I added another little amazon box so it sat high enough. OR use the cardboard from the box to make a template for where the drill holes need to be (it is easier to hold cardboard than a range hood!)