2007BaltA..16...26P

Symbiotic binaries form a diverse class of interacting binaries that can be used to constrain binary evolution theory. In this contribution we will review some of the major unsolved issues concerning symbiotic binaries, in particular the origin of the orbital-period distribution of S-type symbiotic binaries, their possible relation to a sub-class of Type Ia supernovae and the stability of mass transfer. We will then present some recent observations of Mira suggesting that even very wide symbiotic experience a new form of Roche-lobe overflow, ``wind Roche-lobe overflow''. We will present preliminary hydrodynamical simulations of this type of mass transfer and discuss its implications for the shaping of (proto-)planetary nebulae, the origin of barium stars and potentially Type Ia supernova progenitors.