It is well known that not every combinatorial configuration admits a geometric realization with points and lines. Moreover, some of them do not admit even realizations with points and pseudolines, i.e. they are 
not topological. In this paper we show that every combinatorial configuration can be realized as a quasiline arrangement on a real projective plane. A quasiline arrangement can be viewed as a map on a closed surface. Such a map can be used to distinguish between two ”distinct” realizations of a combinatorial configuration as a quasiline arrangement. Based on work in progress with several mathematicians including Leah Berman, Juergen Bokowski, Gabor Gevay, Jurij Kovič and Arjana Žitnik.