The spread of the SARS-CoV-2 virus has caused crucial changes in the workplace. Almost two years after the start of the COVID-19 era, new and old psychosocial risks in the workplace threaten workers’ mental wellbeing and represent an occupational health challenge. The aim of this review is to identify the most relevant psychosocial factors, negative or protective, contributing to occupational stress during the current pandemic. A literature search was conducted in PubMed, EMBASE, Cochrane Library, Web of Science, Google Scholar and PsycINFO and a total of 51 articles were deemed suitable for inclusion in the review. Analysis of the retrieved articles revealed five main topics related to psychosocial wellbeing in the workplace: 1. Support from colleagues and organizations; 2. Home–work interface and balance; 3. Changes in workload and work demand; 4. Job competence and appropriate training; 5. Job insecurity and financial stress. All five themes were associated with occupational stress and poor mental outcomes, like anxiety, depression, and burnout symptoms. Peer and organizational support seem to have a major impact on workers’ mental wellbeing. Recognizing these factors and projecting interventions that mitigate their effects or boost their efficacy is a fundamental step towards dealing with COVID-19 in the workplace, or any such future emergencies.