The installation type of a range hood appliance defines its purpose and design.

Wall Mounted - these are some of the more preferred range hood styles. These are mounted with one surface flush to the wall and typically have a visible exhaust or upward portion to them. These are also among the best looking and most design worthy range hoods.
Under Cabinet - among the most common style, these units are installed below the cabinets above your cooking range and take up a minimal amount of space.
Insert - these range hoods are literally inserted in the base of the upper cabinet space and have no front sections showing, these units are perfect for a kitchen with minimal area to work with or where you want to hide the range hood.
Microwave - these are range hoods that are also microwave units mounted directly above the cooking surface, these are dual purpose units that give you the microwave appliance and the range hood utility in one.
Downdraft - these units pop-up from an island or back splash and draw the exhaust down through the floor or cabinet to expel it. These are great for islands with cook tops of them where you want to preserve your open ceiling space or view.
Island - range hoods for islands typically drop down from the ceiling and are made to look good from all sides. These units only attach to the ceiling.

Smeg Range Hoods