This chapter surveys the theory of optimal insurance contracts under moral hazard. Moral hazard leads to insurance contracts that offer less than full coverage of losses. What form does the optimal insurance contract take in sharing risk between the insurer and the individual: a deductible or co-insurance of some kind? What are the factors that influence the design of the contract? Posed in the most general way, the problem is identical to the hidden-action principal-agent problem. The insurance context provides structure that allows more specific implications for contract design. We review the static models of optimal insurance under ex ante and ex post moral hazard and the potential for repeated interactions and long-term contracts to mitigate moral hazard. We also discuss optimal insurance for liability risk, under which not just insurance but limited liability offers protection against large losses.