Insurance companies play a very important role in the modern financial system by providing financial protection against various risks to individuals and economic entities. Although they offer risk protection to others, they are also exposed to various business risks every day. Operational risks, which are the subject of this paper, have gained importance following their role in causing multiple insolvencies in the financial industry and subsequently with the introduction of the Solvency II regulation, which places particular emphasis on improving risk management and control. These risks can result from human actions, inadequate processes and systems, and external factors. The research aims to show the significance and complexity of operational risks. The significance of these policies is shown by their ability to lead to significant difficulties in business, substantial financial losses, loss of reputation, and even insolvency of the insurance company. Managing them is extremely challenging, considering they are more difficult to identify, measure, evaluate, and control than most other risks. They include technological risks, and the application of technology is growing yearly in the insurance sector. This paper presents how much capital is allocated for operational and other material risks by Croatia's three leading insurance companies to maintain their financial stability and remain solvent. The paper begins by defining the fundamentals related to insurance and risks. Operational risks, as part of the business risks, are described in detail together with operational risk management systems and internal control systems of insurance companies. The paper also defines the regulation of insurance companies with an emphasis on the Solvency II regulation. The importance of operational risks and their management challenges is described with a detailed analysis of the solvency and financial condition reports for Croatia Osiguranje, Euroherc and Allianz osiguranje. The paper's conclusion emphasizes the significance of operational risks in today's financial system. Data were collected from secondary sources, and the methods used were analysis, description, synthesis, and comparative methods. The work's contribution is displayed in the systematization of the key characteristics of operational risks and in raising awareness about their significance and the increasing challenges of management.