Domains with Non-Compact Automorphism Group: A Survey
  We survey results arising from the study of domains in C^n with non-compact automorphism group. Beginning with a well-known characterization of the unit ball, we develop ideas toward a consideration of weakly pseudoconvex (and even non-pseudoconvex) domains with particular emphasis on characterizations of (i) smoothly bounded domains with non-compact automorphism group and (ii) the Levi geometry of boundary orbit accumulation points.   Particular attention will be paid to results derived in the past ten years. 
A. V. Isaev and S. G. Krantz