  Categorical models of constructive and intuitionistic set theories have flourished over the years.  The notions of topos and sheaf play an  essential role here (see e.g. Fourman 1980 and Fourman and Scott 1980). For an overview of the main concepts, see the entry on  category theory and the references provided there (see in particular the supplement  Programmatic Reading Guide).  For recent developments that relate more specifically to constructive set theories, see e.g. (Simpson 2005) and (Awodey 2008), as well as the web page:  algebraic set theory.