Nowadays, test cases may correspond to elaborate programs. It is therefore sensible to try to specify test cases in order to get a more abstract view of these. This paper explores the notion of test purpose as a way to specify a set of test cases. It shows how test purposes are exploited today by several tools that automate the generation of test cases. It presents the major relations that link test purposes, test cases and reference specification. It also explores the similarities and differences between the specification of test cases, and the specification of programs. This opens perspectives for the synthesis and the verification of test cases, and for other activities like test case retrieval.