In recent years, biobanking infrastructure has been gradually built in Central and Eastern Europe. The long-term success of biobanking, however, depends on the public’s engagement in the process. The available evidence indicates low informedness and hesitancy towards biobanking in CEE. Understanding of driving forces and barriers in laypeople’s participation in biobanking is thus a key challenge. The present paper aims to (1) summarize the available evidence, especially from the CEE countries, on public awareness and willingness to participate in biobanking, (2) provide the results of a systematic review on psychological correlates of engagement in biobanking in CEE, and (3) highlight the most pressing issues regarding the available evidence. In general, public awareness, biobanks’ communication and cooperation, ethical and legal regulations, and institutional/governmental trust seem to determine public engagement in biobanking the most. However, cultural specifics are likely to play a major role. Unfortunately, there is a dearth of behavioral data on this topic for the CEE countries. General recommendations on how to increase laypeople’s participation in biobanking are discussed. For the field to progress, future in-depth research on this topic conducted in the CEE countries is needed.