There is a mature body of work in logic aiming to characterize logical formalisms in terms of their structural or model-theoretic properties. The origins of this work can be traced to Alfred Tarski’s program to characterize metamathematical notions in “purely mathematical terms” and to Per Lindström’s abstract characterizations of first-order logic. For the past forty years, rule-based logical languages have been widely used in databases and in related areas of computer science to express integrity constraints and to specify transformations in data management tasks, such as data exchange and ontology-based data access. The aim of this talk is to present an overview of more recent results that characterize various classes of rule-based logical languages in terms of their structural or model-theoretic properties.