The opioid abuse epidemic represents a major public health threat to global populations. The role social media may play in facilitating illicit drug trade is largely unknown due to limited research. However, it is known that social media use among adults in the US is widespread, there is vast capability for online promotion of illegal drugs with delayed or limited deterrence of such messaging, and further, general commercial sale applications provide safeguards for transactions; however, they do not discriminate between legal and illegal sale transactions. These characteristics of the social media environment present challenges to surveillance which is needed for advancing knowledge of online drug markets and the role they play in the drug abuse and overdose deaths. In this paper, we present a computational framework developed to automatically detect illicit drug ads and communities of vendors. The SVM- and CNN- based methods for detecting illicit drug ads, and a matrix factorization based method for discovering overlapping communities have been extensively validated on the large dataset collected from Google+, Flickr and Tumblr. Pilot test results demonstrate that our computational methods can effectively identify illicit drug ads and detect vendor-community with accuracy. These methods hold promise to advance scientific knowledge surrounding the role social media may play in perpetuating the drug abuse epidemic.