Even though we're in a rental, we've been so tempted to install a cheap recirculating hood over the stove, just to have some air filtration and circulation going on. It probably wouldn't be worth it, though.
So instead we keep good air circulation in the kitchen and open a window or door if need be when cooking at high heats. We also tend to scrub our backsplash and light above the stove quite a lot.
What about you? Do you have a vent hood, or, as in the case of many rentals and apartments, you have no way of venting to the outside and therefore a puny recirculating hood or no vent at all?
Do you have good recommendations for a recirculating range hood, or for a regular vent for those readers lucky enough to be able to install the real thing?
Here's a little of our past coverage of range hoods and venting: