Although not a member of either the European Union or the European Economic Area, the Vatican City maintains an open border with Italy and is treated as part of the Schengen Area. Since the Vatican City is only accessible via Italy, entering the Vatican City is not possible without entering the Schengen Area first; hence Schengen visa rules apply de facto. The Vatican City does not allow any foreign accommodations, and the residence is restricted only to citizens.[1]
Bilateral agreements
Vatican City signs independent visa-free agreements which are of symbolic value for foreign citizens but do have effect on Vatican passport holders.[2][3]
See also
Wikivoyage has a travel guide for Vatican.