The world is currently experiencing one of the worst pandemics of this century. During this period, cybersecurity becomes even more important, because during a pandemic, the cyber environment is very favorable for malevolent attackers, and society is facing a huge increase in cyberattacks. This article analyzes the general picture of cybersecurity threats during the COVID-19 pandemic, discusses the legislative and technological aspects of personal data security, highlights and briefly describes the new cyber threats that arise in digital pandemic monitoring systems. Measures to combat infodemia and the role of social media in this matter are being investigated. Finally, recommendations for users and organizations to ensure cybersecurity and proposals for modernization of cybersecurity infrastructure are being developed related to implementation of the concept of work from home. The article uses the methods of systematization, generalization, classification and comparative critical analysis. The obtained results are expected to be very useful for improving the cybersecurity systems in organizations in the context of the new increased requirements during the COVID-19 pandemic and post-pandemic period (pp.12-22).