Biobanks have been heralded as essential tools for translating biomedical research into practice, driving precision medicine to improve pathways for global healthcare treatment and services. Many nations have established specific governance systems to facilitate research and to address the complex ethical, legal and social challenges that they present, but this has not lead to uniformity across the world. Despite significant progress in responding to the ethical, legal and social implications of biobanking, operational, sustainability and funding challenges continue to emerge. No coherent strategy has yet been identified for addressing them. This has brought into question the overall viability and usefulness of biobanks in light of the significant resources required to keep them running. This review sets out the challenges that the biobanking community has had to overcome since their inception in the early 2000s. The first section provides a brief outline of the diversity in biobank and regulatory architecture in seven countries: Australia, Germany, Japan, Singapore, Taiwan, the UK, and the USA. The article then discusses four waves of responses to biobanking challenges. This article had its genesis in a discussion on biobanks during the Centre for Health, Law and Emerging Technologies (HeLEX) conference in Oxford UK, co-sponsored by the Centre for Law and Genetics (University of Tasmania). This article aims to provide a review of the issues associated with biobank practices and governance, with a view to informing the future course of both large-scale and smaller scale biobanks.