In this expository paper we give an overview of some statistical methods for the monitoring of social networks. We discuss the advantages and limitations of various methods as well as some relevant issues. One of our primary contributions is to give the relationships between network monitoring methods and monitoring methods in engineering statistics and public health surveillance. We encourage researchers in the industrial process monitoring area to work on developing and comparing the performance of social network monitoring methods. We also discuss some of the issues in social network monitoring and give a number of research ideas.