Social networks have become popular and useful tools now a day. In the beginning researchers in social networks concentrated in studying static versions. However, the inclusion of time variations made the social networks dynamic. In the present day scenario the social networks are more dynamic than static. The introduction of societal networks by J. Fiksel is an evolutionary step in the study of social networks which originated the concept of dynamic social networks. The term societal network was used by Fiksel in order to distinguish it from the diversified ways in which the term 'social network' was used prior to the 1980s. There seems to be little work done following his approach. In this chapter we introduce the social structures which form the basis of Fiksel's concept and also present his results. Some further study was made by Acharya using the graph theoretic concepts and also he proposed some directions of research. Dynamic social networks are studied recently from different angles. We also present some of these works and propose possible direction of research in this interesting field of research in social networks. © 2014, Springer International Publishing Switzerland.