Morphological case is conventionally defined as a system of marking of a dependent nominal for the type of relationship they bear to their heads. While most linguists would agree with this definition, in practice it is often a matter of controversy whether a certain marker X counts as case in language L, or how many case values language L features. First, the distinction between morphological cases and case particles/adpositions is fuzzy in a cross-linguistic perspective. Second, the distinctions between cases can be obscured by patterns of case syncretism, leading to different analyses of the underlying system. On the functional side, it is important to distinguish between syntactic (structural), semantic, and “pragmatic” cases, yet these distinctions are not clear-cut either, as syntactic cases historically arise from the two latter sources. Moreover, case paradigms of individual languages usually show a conflation between syntactic, semantic, and pragmatic cases (see the phenomenon of “focal ergativity,” where ergative case is used when the A argument is in focus). The composition of case paradigms can be shown to follow a certain typological pattern, which is captured by case hierarchy, as proposed by Greenberg and Blake, among others. Case hierarchy constrains the way how case systems evolve (or are reduced) across languages and derives from relative markedness and, ultimately, from frequencies of individual cases. The (one-dimensional) case hierarchy is, however, incapable of capturing all recurrent polysemies of individual case markers; rather, such polysemies can be represented through a more complex two-dimensional hierarchy (semantic map), which can also be given a diachronic interpretation.