Respondent-driven sampling (RDS) is a link-tracing survey method for sampling members of a hidden or hard-to-reach population such as drug users, sex workers, or homeless people via their social network.  Starting with a set of “seed” subjects, participants use a small number of coupons tagged with a unique code to recruit their social contacts by giving them a coupon.  Subjects report their network degree, but not the identities of their contacts.  RDS is controversial and researchers disagree about whether it can be used to estimate population-level characteristics of hidden risk groups.  In this presentation, I outline four results that permit principled network-based epidemiology from RDS. First, I show that a simple continuous-time model of RDS recruitment implies a well-defined probability distribution on the recruitment-induced subgraph of respondents; the resulting distribution is an exponential random graph model (ERGM).  I develop a computationally efficient method for estimating the hidden graph.  Second, I show that two sources of dependence in the RDS sample — network homophily and preferential recruitment — are confounded. However, it is still possible to make valid inferences via nonparametric graph-theoretic identification regions that permit hypothesis testing. Third, I derive conservative standard errors via graph-theoretic bounds for statistical functionals of the induced subgraph and traits of sampled subjects, including estimators of the population mean. Fourth, I describe a simple technique — based on capture-recapture and the network scale-up method — for estimating the size of a hidden population from an RDS sample. I apply these techniques to RDS studies of drug users in Eastern Europe, Russia, and Lebanon.