Students entering English-medium universities around the world come from diverse linguistic backgrounds and many find it difficult to cope with the language demands of their degree courses. This speech focuses first on the motivations for introducing what are known in Australia as post-entry language assessments (PELAs). I discuss in particular the Diagnostic English Language Needs Assessment (DELNA) at the University of Auckland, which has been successfully implemented throughout the university in the last ten years. This leads to a broader discussion of three significant issues in post-entry language assessment. One is the nature of the construct on which such assessments are based. A related issue is whether a PELA can appropriately be considered "diagnostic" in nature. The third issue is how to undertake the validation of a PELA, particularly with regard to the consequential aspect: does the assessment contribute to enhancing the students' academic language ability?