This article is concerned with the ultimate objectives of genetic biobanks set up to promote the public interest—being the sharing of samples and data for medical research—and the consequences for personal privacy of realising them. Our aim is to chart the values, interests and principles in play, to consider the challenges of realizing biobanking objectives on a global scale, and to propose viable ways forward that ensure, as far as possible, that access provisions remain fit for purpose throughout the entire life of a biobank, while adequately protecting the privacy interests at stake. It is argued that key features in any robust access model must include mechanisms to (a) maintain participant trust in management of the resource and to measure and respond to participants’ expectations, (b) facilitate and promote the sharing of benefits, and (c) respond timeously and effectively to new challenges.