 An influential point of view takes models to be set-theoretic structures. This position can be traced back to Suppes (1960) and is now, with slight variants, held by most proponents of the so-called semantic view of theories (for a discussion of this view, see the entry on  the structure of scientific theories).  There are differences between the versions of the semantic view, but with the exception of Giere (1988) all versions agree that models are structures of one sort or another (Da Costa and French 2000).