Cyber insurance is a complementary mechanism to further reduce the financial impact on the systems after their effort in defending against cyber attacks and implementing resilience mechanism to maintain the system-level operator even though the attacker is already in the system. This chapter presents a review of the quantitative cyber insurance design framework that takes into account the incentives as well as the perceptual aspects of multiple parties. The design framework builds on the correlation between state-of-the-art attacker vectors and defense mechanisms. In particular, we propose the notion of residual risks to characterize the goal of cyber insurance design. By elaborating the insurer's observations necessary for the modeling of the cyber insurance contract, we make comparison between the design strategies of the insurer under scenarios with different monitoring rules. These distinct but practical scenarios give rise to the concept of the intensity of the moral hazard issue. Using the modern techniques in quantifying the risk preferences of individuals, we link the economic impacts of perception manipulation with moral hazard. With the joint design of cyber insurance design and risk perceptions, cyber resilience can be enhanced under mild assumptions on the monitoring of insurees' actions. Finally, we discuss possible extensions on the cyber insurance design framework to more sophisticated settings and the regulations to strengthen the cyber insurance markets.