The first cases of coronavirus 2019 (COVID-19) occurred in Wuhan, China, and rapidly become a public health emergency of international proportions. The disease may cause mild-to-severe acute respiratory syndrome (SARS) and is caused by a SARS-CoV-2 coronavirus infection. The clinical manifestations of COVID-19 include fever, dry cough, fatigue, sputum production, shortness of breath, sore throat, and headache. This article is a narrative review with the aim of analyzing the current literature on postviral olfactory dysfunction (OD) related to SARS-CoV-2 pandemics. Since the initial anecdotal reports from China, international reports on COVID-19 patients have been increasing, describing a 5% to 85% range of loss of smell. To date, the literature is widely heterogeneous regarding the loss of smell; therefore, we advise home isolation measures and/or social distancing, and to carry out diagnostic tests for SARS-CoV-2 when possible in those patients with sudden and severe loss of smell who cannot be promptly evaluated.