Insurance, in general, is a financial contract between the one buying the insurance (also known as the policyholder or insured) and the one providing insurance (known as insurance carrier or insurer). The contract, known as the insurance policy, typically states that the policyholder will pay a regular insurance premium in exchange for a financial compensation, also known as indemnification, in the event of a loss defined in the insurance policy. Insurance is used to manage risks by transferring them to the insurer, and cyber-insurance in particular deals with cyber risks covering direct and indirect damages caused by cyberattacks. The cyber-insurance market is still growing and has been receiving broader interest from research communities and government bodies over the years. This paper provides an overview of cyber-insurance, novel models proposed throughout the years and future challenges to be addressed for cyber-insurance to become a key component of an organisation’s and household’s cyber risk management approach.