The current main world university rankings broadly group the leading research universities of nations. Australia's Go8 universities are generally within the top 250 ranked universities, with several institutions in the top 50-100 on some measures. This recognition is commendable, however imperfect the individual rankings may be. Use is made of rankings by prospective students, governments and universities themselves. There is not always a good alignment between the purposes for which rankings are designed and the ways they are used. All of the rankings are deficient methodologically, and some are seriously flawed. Considerable work needs to be done to overcome the major deficiencies in ranker methods, especially those reliant on reputational surveys and proxy indicators, to give them greater statistical validity and reliability and better representation of disciplinary fields and cross-disciplinary work. Because of the complexity of universities their assignment to ranks will always give a false sense of precision. It would be more appropriate for universities to be banded on the basis of their performance in relation to sets of criteria rather than ranked one after another. Meanwhile, for Australia's leading universities, it is no time for complacency. Their positions are challenged by the rapid rise of universities in Asia and elsewhere. Additionally they face three main public policy threats: under-investment; dilution of investment; and narrow instrumentalism of support. A combination of these three threats in policy for higher education and university research is inimical to sustaining excellence for those universities whose mission is liberal and professional education of high quality in the context of internationally-referenced basic research and nationally-applicable applied research. If these three threats were to be realised in Australian public policy--and they are imminent--the country will not be celebrating for much longer the position of its leading universities in the world league. The construction of rankings is appended. (Contains 10 figures, 17 tables, and 1 box.)