Online social networks such as Facebook, Myspace, and Twitter have experienced exponential growth in recent years. These OSNs offer attractive means of online social interactions and communications, but also raise privacy and security concerns. In this article we discuss the design issues for the security and privacy of OSNs. We find there are inherent design conflicts between these and the traditional design goals of OSNs such as usability and sociability. We present the unique security and privacy design challenges brought by the core functionalities of OSNs and highlight some opportunities of utilizing social network theory to mitigate these design conflicts.