The aim of this work was to conduct a systematic review on psychological behavior in the context of pandemic scenarios during the twenty-first century. We focused on empirical works and brief case reports of H1N1 flu and COVID-19. Our review included 32 papers published both in English or Spanish. We built a set of tables that allowed us to classify the information in four main categories, namely the psychological impact of the pandemic, whether people follow or not official measures to protect themselves against the pandemic, psychological adherence considerations implied as mediators to respect official strategies, and relevant methodological characteristics of the pandemic research. Results show that there are significant impacts on the psychological behavior of people, social groups and organizations in several dimensions, namely emotion, cognition, behavior, mental health, organization and psychosocial factors. In addition, we found that certain social groups experienced a critical psychosocial impact likely due to the pandemic. Psychosocial factors affecting adherence were also identified, which allow us to better understand how health strategies are followed by the population. Different psychosocial suggestions, which emerged from the papers reviewed, were systematized and should be considered as possible pandemic strategies to be implemented.