In the 1970s, C. Fefferman imitated a program of constructing geometric invariants of bounded complex domains by using the canonical Einstein-Kähler metric on it. The program has been generalized to the construction of conformal invariants via complete Einstein metric with prescribed conformal structure on the boundary at infinity. Later, in 1997, J. Maldacena applied this picture to theoretical physics; it is now known as AdS/CFT correspondence and soon become a very active area of research. Then ideas from physics were imported to Fefferman’s original program on complex domains. In this talk, I will explain some of global invariants of strictly pseudoconvex domains recently obtained in this program, including, renormalized volume and Q-prime curvature.