Anosmia, the loss of smell, is a common and often the sole symptom of COVID-19. The onset of the sequence of pathobiological events leading to olfactory dysfunction remains obscure. Here, we have developed a postmortem bedside surgical procedure to harvest endoscopically samples of respiratory and olfactory mucosae and whole olfactory bulbs. Our cohort of 85 cases included COVID-19 patients who died a few days after infection with SARS-CoV-2, enabling us to catch the virus while it was still replicating. We found that sustentacular cells are the major target cell type in the olfactory mucosa. We failed to find evidence for infection of olfactory sensory neurons, and the parenchyma of the olfactory bulb is spared as well. Thus, SARS-CoV-2 does not appear to be a neurotropic virus. We postulate that transient insufficient support from sustentacular cells triggers transient olfactory dysfunction in COVID-19. Olfactory sensory neurons would become affected without getting infected. Keywords: B.1.1.7; COVID-19; SARS-CoV-2; UGT2A1; coronavirus; leptomeninges; olfactory bulb; olfactory receptor; olfactory sensory neuron; sustentacular cell.