The COVID-19 pandemic has affected many aspects of our lives, including mental health. Identifying risk factors and risk groups associated with anxiety, depression, and other emotional disorders for reasons related to the COVID-19 pandemic is highly relevant. This narrative review aims to summarize the evidence to date on risk factors for emotional disorders during the COVID-19 pandemic in order to identify the risk groups of people in need of early psychiatric and psychological assistance, point out the controversial data on the influence of risk factors on emotional disorders in COVID-19, and finally offer recommendations for alleviating symptoms of anxiety, depression, and other emotional disorders in such people. According to the current literature, being under the age of 40, being female, having contact with a COVID-infected person, and watching the news about COVID-19 for more than 3 h a day all increase the likelihood of anxiety, depression, and sleep disturbances. Healthcare workers, particularly nurses, working in the COVID-19 hot zone suffer more from sleep disorders, anxiety, and depression. It is also noted that people with a previous psychiatric history, in addition to increased risks of anxiety and depression, have an increased risk of relapse during the COVID-19 pandemic. The same is true for people who have had episodes of substance abuse in the past. Aside from socioeconomic factors, the mental wellbeing of those who have had COVID-19 is also impacted by biological factors (using anti-COVID-19 drugs, COVID-19-associated immunothrombosis and venous thromboembolism, interferon-gamma-related cytokine storm, etc.), resulting in a wide range of acute and long-term cognitive disorders. During the restricted resource time, the aforementioned risk groups should be prioritized for prevention, early identification, and proper treatment of potential emotional disorders. The risk factors that were found in this narrative review, as well as how they interact and change over time, will help understand why some studies of at-risk groups do not agree with each other, justify new preventive measures, and strengthen existing programs to keep people’s mental health in check during this pandemic and other emergencies.