This paper introduces the notion of adpositions as a grammatical category, their classification by means of function and form, and their grammaticalization across languages. It highlights the fact that the boundary between case and adposition is fuzzy because their concepts are not well delineated and, in addition, because there is no consensus as to their classification typology. It also discusses the relevance of adpositional concepts to human cognition, which renders support to the claim that the general similarity of linguistic systems is due to the overall universality of the ways human cognition operates. It further addresses some typological issues that cause different manifestations of adpositions in individual languages. The last section of the paper provides an overview of the individual contributions to this special issue and briefly discusses the theoretical imports of the findings and generalizations each contribution makes.