"Recirculating" range hoods are basically a consumer fraud. They make noise and thereby create the illusion that they're doing something. They run the exhausted air through a mesh or filter only.....which does, in fact, some good. However, so little good it's hardly worth giving credit. In my experience, I would say in the "better than nothing" category....with the caveat "not much better".

If there's any way in the world you can duct to the outside, do it! Otherwise, just about all the oil-laden vapors from your cooking will be re-deposited on your household surfaces. It has never been different.

Problems? Oh, yes!

If you're selling/moving in a year or so, you may not care. If you're living with it, please, please, please duct to the outside.

exhausting greasy air is good.

Grease specks can be microscopically small. Grease carries food odors.

In my jurisdiction, exterior venting is now code for all new builds and major renos. Cooking is a major source of household pollution, and removing it is very important to maintain air quality in tightly sealed, energy efficient homes.

Wish I could vent the condo to the outside! I will replace the range with something much more powerful, and cooking with the best recirculating I can find is better than not cooking.

A vented hood is helpful, but not essential. We lived with a Blue Star/Garland range and no hood for about eight years, because we could not vent outside from our apartment. Things like searing meat got the apartment smokey, but it wasn't the end of the world. We did have a kitchen window that did help a little.

We has a ventless hood. I agree with others, that the ventless hood is virtually useless. It looked good, but we rarely ran it. All it did was blow the smoke around.

The other thing about not venting, apart from odors, is grime. If the microscopic drops of oil (and food-laden water, e.g. pasta water full of starch) that fly up when you cook are not vented, they have to land somewhere; they will land on your walls, your cabinets, your counters, your floor, and any decorations or things left out (dishes on open shelves etc.). So they will make all those surfaces dirty AND they will create a sticky layer on those surfaces that normal household dust will stick to like glue AND that bacteria can grow in (after all the oil, starch etc. feeds the bacteria).

So it's part a hygiene issue and part just a "dinge" issue. If you don't vent you will have to clean more to keep your kitchen from getting dingy (and STICKY, ick), and cleaning will be more difficult because of the layer of oil, starch etc. And surfaces, especially cabinet and wall surfaces (which are typically more porous than counters and floors), will wear out faster because of this constant cycle of grime/cleaning products/scrubbing.

When heated, oil (grease) can float up invisibly. Microscopic particles, smaller than droplets. This is what you might call the smell of cooking. If you turn on the vent, and open a window to have replacement air, you can cook without letting any smell into the other rooms. Without exhaust venting, if you restrict your cooking style you might keep a clean house that does not get grungy and dingy over time. I've seen a lot of people who live in cold climates who seem to almost naturally adopt cooking styles that create less grease and smells. Then, when they go to restaurants they order type of food that they never cook at home. In this post I have not mentioned smoke, just plain old oil and grease specks. Steam is another subject too.

I know many people who don't use their vents. Their homes are all cleaner than mine (and I always use a good vented hood) but they work harder at it. I've had the recirculating hood things--some have refillable carbon pads to help remove odors which might work. They also have mesh thingies that DO capture grease. You will know this after you clean them. They do something. I think they are considerably better than nothing.

Me, though, I'd vent out.