Human biological materials and related data stored in biobanks are valuable resources for biomedical research. Transparent, effective, and efficient governance structures and procedures for access, compensation, and priority setting are needed, but recent debates indicate challenges in the practical application of such governance processes. This study aimed to assess the practical experiences and attitudes of biobank experts regarding the governance of biosample access, prioritization, and compensation. Qualitative, semi-structured telephone interviews were conducted with 20 biobank directors from eight countries. Respondents highlighted the need for sound governance structures in order to ensure acceptance by all stakeholders (patients/donors, researchers, research funders, public, and others). They stressed practical difficulties in trying to make best use of biomaterials. As biobanks often form part of larger academic and clinical settings, the different and sometimes conflicting interests of researchers, clinicians, patients, funders, and biobank staff currently affect the governance of access decisions. Investments such as intellectual input, financial, and human resources need to be compensated adequately. Biobanks thereby have a dual role stewarding the hosted biosamples and acting as a service provider for local researchers from universities or hospitals. In order to facilitate efficient use of human biological materials, greater harmonization of at least minimum standards for access and compensation are required at both a national and an international level.