The article analyzes the impact of the COVID-19 pandemic on the world insurance market and some European countries. Separated economic indicators of the impact of the COVID-19 pandemic on the insurance business of the world are singled out. It was determined that the impact of the COVID-19 pandemic inspired declining incomes of insurers and households, rising unemployment, declining demand for insurance services, a significant decline in productivity of insurance companies, uncertainty about the future development of the insurance industry and the effects of the pandemic. The experience of the world insurers' struggle against the consequences of the COVID-19 pandemic has been studied and generalized. The latest tools that have allowed insurers around the world to mitigate or mitigate the negative impact of the crown crisis, in particular, are: the development of new insurance products; increasing the level of requirements for insurance services in terms of its relevance, price flexibility, mobility and transparency; transition of insurers to online sales of insurance services and online payments for insurance cases; direct funding of specific means of combating COVID-19; use of the latest technologies and innovative methods in the insurance business; introduction of a new mode of staff work in the activities of insurance companies. The transition of insurers to online sales of insurance services and online payments has revealed many unresolved issues regarding the insurer's cybersecurity. Insurers are forced to improve existing technologies and methods of control, to intensify training and information activities. The Crown Crisis has significantly increased the importance of modern underwriting. Therefore, insurers around the world are using the capabilities of artificial intelligence, alternative data sources and better forecasting models. Greater understanding of pandemic processes, gaining experience is needed not only to accelerate the way out of the modern pandemic, but also to form a stable insurance system to the inevitable future challenges. The study of positive experience in the functioning and development of insurance markets around the world in crises and shocks is useful for application in national practice.