Recent trends in biobanking indicate that the practices associated with the collection and use of human tissue samples and related health information are increasingly becoming premised on networks of biobanks. These networks and partnerships often involve international collaborations, as well as public–private partnerships. This article reports on the results of a study of people's attitudes towards biobanking and the biomedical use of tissue samples in Finland. Three approaches were used to study these attitudes: a population-based survey, focus group interviews among members of patient organizations and short interviews with research participants. In particular, we look at the attitudes of respondents in these three studies towards the use of tissue samples and use them as a catalyst to discuss two dimensions of biomedical research: public/private and domestic/international. Our discussion highlights how notions of value related to the use of tissue samples vary and provide contrasting perspectives and ambiguity that people may have towards various types of research partnerships and the benefits that may arise from them.