In noncommutative geometry, the correspondence between algebra and geometry is used to study e.g. quotient spaces in topology or algebraic geometry, that would otherwise be difficult to describe. We look at certain examples from the point of view of topos theory: the underlying topos of the Connes--Consani Arithmetic Site, a generalization using 2x2 integer matrices, and toposes of sheaves on a category of Azumaya algebras. We try to use methods that can easily be generalized to other situations. The relation to some topics in number theory and representation theory will be discussed.