This work aims to present our current best physical understanding of common-envelope evolution (CEE). We highlight areas of consensus and disagree- ment, and stress ideas which should point the way forward for progress in this important but long-standing and largely unconquered problem. Unusually for CEE-related work, we mostly try to avoid relying on results from population synthesis or observations, in order to avoid potentially being misled by previous misunderstandings. As far as possible we debate all the relevant issues starting from physics alone, all the way from the evolution of the binary system immediately before CEE begins to the processes which might occur just after the ejection of the envelope. In particular, we include extensive discussion about the energy sources and sinks operating in CEE, and hence examine the foundations of the standard energy formalism. Special attention is also given to comparing the results of hydrodynamic simulations from different groups and to discussing the potential effect of initial conditions on the differences in the outcomes. We compare current numerical techniques for the problem of CEE and also whether more appropriate tools could and should be produced (including new formulations of computational hydrodynamics, and attempts to include 3D processes within 1D codes). Finally we explore new ways to link CEE with observations. We compare previous simulations of CEE to the recent outburst from V1309 Sco, and discuss to what extent post-common-envelope binaries and nebulae can provide information, e.g. from binary eccentricities, which is not currently being fully exploited.

By assuming an aspherical stellar wind with an equatorial disc from a red giant, we investigate the production of Type Ia supernovae (SNe Ia) via a symbiotic channel. We estimate that the Galactic birthrate of SNe Ia via the symbiotic channel is between 1.03 × 10−3 and 2.27 × 10−5 yr−1, while the delay time of SNe Ia has a wide range from ∼0.07 to 5 Gyr. The results are greatly affected by the outflow velocity and mass‐loss rate of the equatorial disc. Using our model, we discuss the progenitors of SN 2002ic and SN 2006X.