Modular operads were introduced, in joint work with Kapranov, for two reasons: to understand the axiomatization of quantum field theory in two dimensions, and to give a natural setting for Kontsevich's graph complexes. In this talk, I show how to incorporate an open sector into the definition of modular operads. At the same time, I present a new point of view on modular operads, in which the role of representations of the symmetric group S_n is taken by representations of the mapping class groups for surfaces with boundary.