Implications in Formal Concept Analysis (FCA), Horn clauses in Logic, and Functional Dependencies (FDs) in the Relational Database Model, are very important dependency types in their respective fields. Moreover, they have been proved to be equivalent from a syntactical point of view. Then notions and algorithms related to one dependency type in a field can be reused and applied to another dependency type in the other field. One of these notions is that of cover, also known as a base or basis, i.e., a compact representation of a complete set of implications, FDs, or Horn clauses. Although the notion of cover exists in the three fields, the characterization and the related uses of a cover are different. In this paper, we study and compare, from an FCA perspective, the principles on which rely the most important covers in each field. Finally, we discuss some open questions that are of interest in the three fields, and especially to the FCA community.