Instance independence is a critical assumption of traditional machine learning methods contradicted by many relational datasets. For example, in scientific literature datasets there are dependencies among the references of a paper. Recent work on graphical models for relational data has demonstrated significant performance gains for models that exploit the dependencies among instances. In this paper, we present relational dependency networks (RDNs), a new form of graphical model capable of reasoning with such dependencies in a relational setting. We describe the details of RDN models and outline their strengths, most notably the ability to learn and reason with cyclic relational dependencies. We present RDN models learned on a number of real-world datasets, and evaluate the models in a classification context, showing significant performance improvements. In addition, we use synthetic data to evaluate the quality of model learning and inference procedures.