Wasps live in nests constructed of different materials depending on the species.
More Info: The typical home of the wasp is known as a "nest", not to be confused with the "hives" of bees. There are several different species of wasps generally belonging to two social orders, solitary and social.
The nest of a solitary wasp is much more diverse than any other kind. Some, including the mud daubers and pollen wasps, build their home from mud cells in a covered area. These are typically seen on the side of a wall or house. Potter wasps, another solitary breed, construct using mud cells as well, often attached to twigs. The majority of the other predatory wasps make home in the earth's soil or into the stem of plants. Then there are others who do not make a nest at all, but instead enjoy resting in holes or cracks that have already been created. An example would be cavities in wood.
Social wasps, on the other hand, are in a separate category when it comes to nesting. These wasps have a specific queen who is the original creator of the next. She builds her home to the approximate size of a walnut, and then her colony takes up residence to continue the process. The females continually work on the nest.
The queen wasp begins the process of building her next by making an initial layer, also called a canopy, and continuing the process outwards until the end of the hole or cavity is reached. Underneath this cavity is where the queen builds a sturdy stalk where individual hives are then constructed. This is where the eggs are laid. This process of building tiers and places to lay eggs is repeated constantly. The queen only works on her nest until enough female workers have been hatched, at that time her sole job will be that of reproduction.