Most real-world data is stored in relational form. In contrast, most statistical learning methods work with "flat" data representations, forcing us to convert our data into a form that loses much of the relational structure. The recently introduced framework of probabilistic relational models (PRMs) allows us to represent probabilistic models over multiple entities that utilize the relations between them. In this paper, we propose the use of probabilistic models not only for the attributes in a relational model, but for the relational structure itself. We propose two mechanisms for modeling structural uncertainty: reference uncertainty and existence uncertainty. We describe the appropriate conditions for using each model and present learning algorithms for each. We present experimental results showing that the learned models can be used to predict relational structure and, moreover, the observed relational structure can be used to provide better predictions for the attributes in the model.