Uncertain network optimization is the study of network optimization with uncertain data which we often meet in decision making under the presence of uncertainties. The main purpose of this manuscript is to present a state-of-the-art review on the recent advances in uncertain network optimization and to show the general uncertain network optimization models based on an uncertainty theory. Some classical network optimization topics in an uncertain environment are revisited, and some challenging topics in future research are addressed in the field of uncertain network optimization. This paper divides uncertain network optimization into two main directions. One line of research deals with network optimization problems with an uncertain topology structure, and another line of research concerns the handling of network optimization with uncertain weights.