Since its outbreak, in December, 2019, in the Chinese city of Wuhan, coronavirus disease 2019 (COVID-19), caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has evolved into an ongoing global pandemic. Due to the novel antigenic properties of this virus, the world population could not develop immunity effectively and this led to the subsequent spread of COVID-19. This caused an unprecedented emergency situation with significant negative effects on health and well-being both on an individual and societal level. Apart from health, economic and social consequences, the impact of this pandemic on mental health is increasingly being reported in the scientific literature. The present review aimed to provide a comprehensive discussion of the possible neurological and neuropsychiatric manifestations of SARS-CoV-2, together with the related underlying molecular pathways. In addition, the present review focused on populations which are at a higher risk of developing psychiatric disturbances due to the COVID-19 pandemic and discussed possible routes of clinical management and therapeutics to minimize the burden associated with psychiatric disorders. Moreover, research findings exploring the prevalence of COVID-19-related post-traumatic stress disorder (PTSD) symptoms across vulnerable groups, including children, adolescents and COVID-19 survivors are presented, with particular emphasis on those with severe disease who required hospitalization and/or intensive care unit admission. Based on the available literature, the identification of potential determinants associated with PTSD across the different populations is underlined. Lessons learnt from the pandemics across the globe together with the ongoing research on COVID-19 and its impact on mental health, highlight the utmost importance for evidence-based, proactive and targeted interventions in high-risk groups aiming to mitigate the risks and manage vulnerabilities.