Projective duality identifies arrangements of n lines in the projective plane and arrangements of n points in the dual projective plane. We ask: how does projective duality behave under degenerations? Kapranov introduced the compactified moduli space of line arrangements, later studied by Lafforgue, Keel-Tevelev, and others. On the other hand, compactified moduli space of point arrangements was introduced by Gerrizen and Piwek. In joint work with Luca Schaffler, we investigate how these two moduli spaces are related.