Bayesian Networks are one of the most popular formalisms for reasoning under uncertainty. Hierarchical Bayesian Networks (HBNs) are an extension of Bayesian Networks that are able to deal with structured domains, using knowledge about the structure of the data to introduce a bias that can contribute to improving inference and learning methods. In effect, nodes in an HBN are (possibly nested) aggregations of simpler nodes. Every aggregate node is itself an HBN modelling independences inside a subset of the whole world under consideration. In this paper we discuss how HBNs can be used as Bayesian classifiers for structured domains. We also discuss how HBNs can be further extended to model more complex data structures, such as lists or sets, and we present the results of preliminary experiments on the mutagenesis dataset.