While biobanks are established explicitly as scientific infrastructures, they are de facto political-economic ones too. Many biobanks, particularly population-based biobanks, are framed under the rubric of the bio-economy as national political-economic assets that benefit domestic business, while national populations are framed as a natural resource whose genomics, proteomics, and related biological material and national health data can be exploited. We outline how many biobanks epitomize this ‘neoliberal’ form of science and innovation in which research is driven by market priorities (e.g., profit, shareholder value) underpinned by state or government policies. As both scientific and political-economic infrastructures, biobanks end up entangled in an array of problems associated with market-driven science and innovation. These include: profit trumping other considerations; rentiership trumping entrepreneurship; and applied research trumping basic research. As a result, there has been a push behind new forms of ‘post-neoliberal’ science and innovation strategies based on principles of openness and collaboration, especially in relation to biobanks. The proliferation of biobanks and the putative transition in both scientific practice and political economy from neoliberalism to post-neoliberalism demands fresh social scientific analyses, particularly as biobanks become further established in fields such as oral health and personalized dentistry. To the best of our knowledge, this is the first analysis of biobanks with a view to what we can anticipate from biobanks and distributed post-genomics global science in the current era of oral health biomarkers.