Data dependencies are integrity constraints that the data of interest must obey. During the 1980s, János Makowsky made a number of contributions to the study of data dependencies; in particular, he was the first researcher to characterize data dependencies in terms of their structural properties. The goal of this article is to first present an overview of Makowsky’s work on characterizing certain classes of data dependencies and then discuss recent developments concerning characterizations of broader classes of data dependencies.