The field of precision medicine allows for tailor-made treatments specific to a patient and thereby improve the efficiency and accuracy of disease prevention, diagnosis, and treatment and at the same time would reduce the cost, redundant treatment, and side effects of current treatments. Here, the combination of organ-on-a-chip and bioprinting into engineering high-content in vitro tissue models is envisioned to address some precision medicine challenges. This strategy could be employed to tackle the current coronavirus disease 2019 (COVID-19), which has made a significant impact and paradigm shift in our society. Nevertheless, despite that vaccines against COVID-19 have been successfully developed and vaccination programs are already being deployed worldwide, it will likely require some time before it is available to everyone. Furthermore, there are still some uncertainties and lack of a full understanding of the virus as demonstrated in the high number new mutations arising worldwide and reinfections of already vaccinated individuals. To this end, efficient diagnostic tools and treatments are still urgently needed. In this context, the convergence of bioprinting and organ-on-a-chip technologies, either used alone or in combination, could possibly function as a prominent tool in addressing the current pandemic. This could enable facile advances of important tools, diagnostics, and better physiologically representative in vitro models specific to individuals allowing for faster and more accurate screening of therapeutics evaluating their efficacy and toxicity. This review will cover such technological advances and highlight what is needed for the field to mature for tackling the various needs for current and future pandemics as well as their relevancy towards precision medicine.