You can travel to non schengen countries with a schengen visa. At least to countries which have active applications to become schengen members e.g. Cyprus. It's

You can travel to non schengen countries with a schengen visa. At least to countries which have active applications to become schengen members e.g. Cyprus. It's just that Cyprus can't issue a schengen visa. Partly one of the reasons Cyprus doesn't get as many refugees as Greece even though being geographically much closer to Syria and Turkey.