Each year funding agencies and academic institutions spend millions of dollars and euros on biobanking. All funding providers assume that after initial investments biobanks should be able to operate sustainably. However the topic of sustainability is challenging for the discipline of biobanking for several major reasons: the diversity in the biobanking landscape, the different purposes of biobanks, the fact that biobanks are dissimilar to other research infrastructures and the absence of universally understood or applicable value metrics for funders and other stakeholders. In this article our aim is to delineate a framework to allow more effective discussion and action around approaches for improving biobank sustainability. The term sustainability is often used to mean fiscally self-sustaining, but this restricted definition is not sufficient for biobanking. Instead we propose that biobank sustainability should be considered within a framework of three dimensions - financial, operational, and social. In each dimension, areas of focus or elements are identified that may allow different types of biobanks to distinguish and evaluate the relevance, likelihood, and impact of each element, as well as the risks to the biobank of failure to address them. Examples of practical solutions, tools and strategies to address biobank sustainability are also discussed.