A range of imperatives underpin university selection practices. These include demonstrating merit based on prior academic achievement and supporting successful graduate outcomes in the professions and in broader fields of endeavour. They also include improving diversity of participation and equality of educational opportunity. Selection for admission therefore involves selecting for student characteristics associated with success at university and also for those associated with the desired mix of students. Finally, fair and transparent selection practices are of particular importance in the context of expanded enrolments and also for courses where the number of applications exceeds the number of places available. While a move toward a "demand driven" funding model for undergraduate enrolments in Australia might imply a shift in emphasis from selection to recruitment in university admissions, selection to courses for which there is high demand will remain necessary and the need for measures to help ensure equity of participation will remain. This paper reviews criteria and strategies in student selection and the implications of their use for equity of participation in higher education and the prospects for student success. The paper offers an analysis of the strengths and weaknesses of criteria for prior academic achievement, tests of aptitude and preparedness and broader criteria used in university selection. The aim of this paper is to support informed discussion regarding the development and improvement of university selection criteria and practices, recognising the common challenges universities face in fostering diversity of participation and student success in an expanding tertiary education environment. Appended are: (1) Types of University (as grouped in Undergraduate Applications, Offers and Acceptances 2009); (2) University of California "Comprehensive Review" Selection Criteria; and (3) Studies of the predictive validity of tertiary entrance rank in Australia. (Contains 7 figures, 7 tables, and 16 footnotes.) [This paper was prepared for the Group of Eight.]