Although the relative importance of airborne transmission of the SARS-CoV-2 virus is controversial, increasing evidence suggests that understanding airflows is important for estimation of the risk of contracting COVID-19. The data available so far indicate that indoor transmission of the virus far outstrips outdoor transmission, possibly due to longer exposure times and the decreased turbulence levels (and therefore dispersion) found indoors. In this paper we discuss the role of building ventilation on the possible pathways of airborne particles and examine the fluid mechanics of the processes involved.