In many languages (e.g. Latin, Greek, Russian, Turkish, German) the relationship of a noun phrase to the rest of a sentence is indicated by altered forms of the noun. The possible relationships are called (surface) "cases." Because (1) it is difficult to specify semantic-free selection rules for the cases, and (2) related phenomena based on prepositions or word order appear in apparently case-less languages, many have argued that studies of cases should focus on meaning, i.e. on "deep cases." A representative sample of proposed case systems is examined. Issues such as surface versus deep versus conceptual level of cases, and the efficiency of the representations implicit in a case system, are also discussed. (Author)