Keplerian orbits can be characterized as minimizers of some action functional on function spaces with natural topological or boundary constraints. This fact is useful in variational construction of periodic orbits for the n-body and n-center problems. The elliptic case, settled by W. Gordon in 1977, is considerably well-known. Parabolic case is less well-known, and hyperbolic case is virtually unknown. In this talk I will briefly outline those known facts, and describe my proof for the minimizing property of hyperbolic orbits.