  This work aims to present our current best physical understanding of
common-envelope evolution (CEE). We highlight areas of consensus and
disagreement, 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.
