Understanding the dynamics and functioning of biological systems is one of the most challenging tasks faced in modern science. An important problem in practice regards how to accurately infer the underlying cause-and-effect (i.e., causal) network from observational data, especially when the underlying system consists of a large number of interacting components and the dynamics is intrinsicaly nonlinear. Utilizing our recently developed theory of causation entropy (J. Sun, D. Taylor, and E. M. Bollt, SIAM Journal on Applied Dynamical Systems 14, 73–106, 2015), we devised an efficient computational approach of optimal causation entropy (oCSE) to infer causal networks from data, and demonstrate its effectiveness using both synthetic and experimental data.