Biobanks have during last two decades gained an important role in the whole process of biomedical research and health care not only in Europe but also worldwide. Biobanks are one of the pillars in personalised medicine tackling all its aspects such as prevention, diagnosis, treatment and monitoring closely the specific characteristics of an individual patient. The current and future power of biobanks is the amount of samples of high-quality and related information available for current and future research of diseases, for optimising patients´ prevention, diagnosis, treatment and monitoring. The material stored in biobanks is a treasure for future technologies that will be able to utilise the currently uncovered information and knowledge. A great and growing number of samples and related information also opens new ways in how to tackle the big data problems and population studies. Biobanks play a substantial role in drug discovery, development and validation. Biobanks are not only an issue of biomedical research, but are becoming a public issue involving patients, to actively participate in biobanking with respect to ethical, legal and social issues. And, finally, biobanking as a multidisciplinary and modern field of science requires appropriate education at all levels of society. To be a world leader in the field of biobanking requires wide international and interdisciplinary collaboration. The topic-dedicated programmes released by the European Commission sustainably support biobank development in Europe and the main tool is the biggest European Union (EU) research and innovation programme ever—Horizon 2020. This article reviews the main Horizon 2020 biobanking projects, financing schemes and the future perspectives.