The main neurological manifestation of COVID-19 is loss of smell or taste. The high incidence of smell loss without significant rhinorrhea or nasal congestion suggests that SARS-CoV-2 targets the chemical senses through mechanisms distinct from those used by endemic coronaviruses or other common cold-causing agents. Here we review recently developed hypotheses about how SARS-CoV-2 might alter the cells and circuits involved in chemosensory processing and thereby change perception. Given our limited understanding of SARS-CoV-2 pathogenesis, we propose future experiments to elucidate disease mechanisms and highlight the relevance of this ongoing work to understanding how the virus might alter brain function more broadly.