This paper explores the cognitive semantics of the typological category “possession” using the Natural Semantic Metalanguage (nsm) approach. At the macro level, we argue that “possession” is not a unitary cognitive category for speakers, but instead represents an aggregation of diverse semantic schemas which center around three distinct conceptual anchor points: ownership, body-parts, and kinship relations. It is shown how each of these conceptual anchor points can be clearly identified using the nsm metalanguage of semantic primes and molecules. At the micro level, the paper undertakes a close examination of the cognitive semantics of English s-genitives in the frame [THIS SOMEONE’S] SOMETHING, e.g. Mary’s ring, Mary’s shoes, Mary’s drawing, Mary’s plate, Mary’s train. It is argued that the wide range of use of the s-genitive can be captured in a set of five semantic schemas, which constitute a network of grammatical polysemy.