The Coronavirus Disease 2019 (COVID-19) pandemic has surprised health authorities around the world producing a global health crisis. This research discusses the main psychosocial stressors associated with COVID-19 in the literature, and the responses of global public mental health services to these events. Thus, a consensus and critical review were performed using both primary sources, such as scientific articles and secondary ones, such as bibliographic indexes, web pages, and databases. The main search engines were PubMed, SciELO, and Google Scholar. The method was a systematic literature review (SLR) of the available literature regarding mental health services during the COVID-19 pandemic to conduct the present narrative review. Different stressors are identified in this pandemic, from psychophysiological, confinement, to social and work. Depending on the level of severity and the country of origin, various interventions have been applied that mark different ways of returning to normality and preparing new interventions. This new stressor has a direct impact on the mental health of the population, provoking governments, and health services to become more flexible, innovate and adapt to the changing situation. The use of technology and mass media could be an important tool in this aim. Independent of this, preparing the general population for possible future waves of the pandemic is currently the best measure to mitigate more serious effects on the mental health of the population.