The public release of generative artificial intelligence (GAI) tools (e,g. ChatGPT) has had a disruptive effect on the assessment practices of higher education institutions (HEIs) worldwide. Concerns have largely been associated with academic integrity, cheating and plagiarism. HEIs have had to develop guidelines in response to GAI. As many of these guidelines were developed in haste and could affect a large number of instructors and students, there is a need to examine their content, coverage and suitability. This review examines the extent to which the world's 50 top-ranking HEIs have developed or modified their assessment guidelines to address GAI use and, where guidelines exist, the primary content and advice given to guide instructors in their GAI assessment design and practices. The findings show that just under half of the institutions have developed publicly available guidelines. The guidelines cover three main areas: academic integrity, advice on assessment design, and communicating with students. Among the suggestions for teachers on assessment design, two appear particularly pertinent in helping develop effective assessment tasks and developing learners’ AI-literacy: first, running assessment tasks through GAI to check the extent to which the tool can accomplish the task and, second, having students use GAI as part of the assessment process. Overall, the review suggests that HEIs have come to accept the use of GAI and drafted assessment guidelines to advise instructors on its use. In the article, we argue that it may be beneficial to embrace GAI as a part of the assessment process since this is the reality of today's educational and job landscape. This will require instructors to develop a new competence - generative artificial intelligence assessment literacy - which is conceptualised in this article.