While there are recirculating range hoods on the market, it's much better to install a vented range hood. The recirculating models simply pull air from the room, pass it over a charcoal vent and then put the air back into the room. Vented hoods take the polluted air out of the room via a duct system through the walls or attic space. Typically, building codes for new kitchens require that outdoor ventilation be part of any range hood installation. Retrofitted kitchen vent ductwork may run through the backs of cabinets to the outdoors rather than tearing out walls. In any installation, the longer the distance to the outside, the less effective the range hood is going to be at removing pollutants from the air.
Each type of cook top makes specific recommendations for the distance between the burners and the range hood. Generally speaking, 30 inches is sufficient. There must be enough space for any cabinets or soffits above the range hood. The width and depth of the range hood should be at least the same size as the range top. It's possible to install a larger size range hood, especially with an island range, but it's never a good idea to install a hood smaller than the cook top.
Cubic feet per minute (CFM) measures the amount of airflow out of the range hood. 100 CFM per 10,000 British thermal units (BTU) is the general measurement for a gas range. There should be enough CFM to handle the emissions if all burners are operating on high at the same time. For an electric range, the CFM measurement comes from the width of the stove. There should be 100 CFM for every 10 inches of stove-top width.
While it may not be a requirement for building codes, keeping the Sone rating to a minimum may be an important requirement to those who use the range hood and work around it. The Sone rating measures the sound output of the range hood. The lower the Sone rating, the less noise the vent hood makes.