The pandemic caused by Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is receiving worldwide attention, due to the severity of the disease (COVID-19) that resulted in more than a million global deaths so far. The urgent need for vaccines and antiviral drugs is mobilizing the scientific community to develop strategies for studying the mechanisms of SARS-CoV-2 infection, replication kinetics, pathogenesis, host–virus interaction, and infection inhibition. In this work, we review the strategies of tissue engineering in the fabrication of three-dimensional (3D) models used in virology studies, which presented many advantages over conventional cell cultures, such as complex cytoarchitecture and a more physiological microenvironment. Scaffold-free (spheroids and organoids) and scaffold-based (3D scaffolding and 3D bioprinting) approach allow the biofabrication of more realistic models relevant to the pandemic, to be used as in vitro platforms for the development of new vaccines and therapies against COVID-19.