The relationship between the metrical grid and the prosodic hierarchy and the relation between prosodic structure and syntactic structure are both relationships and relations of Correspondence. Correspondence is a representational link between two representational objects. Entries on the metrical grid and instances of prosodic categories may correspond, and instances of prosodic categories and instances of syntactic categories may correspond. Mapping is the correspondence relation between instances of prosodic categories and entries on the metrical grid. The mapping relation is one of the key factors influencing the grid’s construction. Mapping is governed by a handful of key principles, including Hierarchy Coordination. The prosodic hierarchy and the metrical grid are both hierarchies and they map to each other as hierarchies. Mapping is required by the violable MAP family of constraints, constraints that require prosodic categories to map to grid entries. The MATCH family of constraints requires faithful correspondence between prosodic categories and syntactic or morphological categories. It requires both that the correspondence relation exist and that that correspondents share key elements. Simple MATCH constraints require correspondents to have exactly the same set of terminal elements. LexMatch constraints require correspondents to have the same set of lexical terminal elements. LexMatch constraints ignore functional terminal elements.