Countertop Microwaves
Countertop microwaves sit on the countertop and come in a variety of sizes. Unless they specifically say they can, countertop units can not usually be installed under a cabinet or over the range.

Over the Range Microwaves
Also called microhoods these are a combination of a microwave and a vent hood for a range. They usually come with a charcoal filter to help remove cooking odors from the air. They need to be installed so that there is at least 2 feet between the top of the range and the bottom of the microwave.

Convection Microwaves
Convection microwaves can cook using either the traditional microwave method or using the convection method. Microwaves cook by exposing the food to microwave radiation. The radiation energizes water molecules in the food, and the friction caused by their rapid vibration then heats the food around them. Convection ovens work by forcing heated air, via fans located in the back of the oven wall, over and around the food. This is more like traditional oven cooking, but it is faster, more even, and requires a lower temperature. Convection ovens can actually bake food, whereas microwaves can not.

Built-In Microwaves
Also called Undercabinet or Over-the-Counter microwaves, these can be installed into an open space in cabinetry, or bolted to the bottom of a cabinet above a counter. They can not, however, be installed over a range. Some of them can also be used as countertop models, but only if they specifically say this.