Studies of static complex networks have brought significant progress in revealing the mechanism for forming and evolving of social networks, information networks, and biological networks. However, many real word networks change with time and this type of networks is the so called dynamic networks. This paper focuses on dynamic networks to study the related pattern mining method and its applications in biological and social networks. First, the study analyzes the topological properties of the dynamic networks. Then we make a comparison and analysis to the algorithms and models for variety of pattern mining in dynamic networks. Specifically, we analyze the dynamics properties of biological and social networks. Based on this property, we study the biological networks related pattern mining problems, such as dynamic function module, pattern evolution and complex diseases associated pattern, the dynamic pattern in social network. Finally, some key problems and challenges in biological and social network are highlighted, as well as the future research directions.