In recent years, with the rapid development of manufacturing, information, and management technology, advanced manufacturing systems (AMSs) have become increasingly more and more complex, which hinders the wider applications of many key theories and technologies in AMSs. Fortunately, in the last two decades, some dramatic advances have been made in the field of statistical physics theories, along with the extensive applications of complex network. It has provided an alternative approach to analyze AMSs. Many recent studies have focused on the theory of complex networks to describe and solve complicated manufacturing problems. Based on a great number of relevant publications, this paper presents an up-to-date literature review with the identified outstanding research issues, future trends and directions. Three critical issues are summarized after this investigation: (a) the focused areas of AMSs that have deployed the theory of complex networks, (b) the addressed issues and the corresponding approaches, and (c) the limitations and directions of the existing works.