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This chapter provides an introduction to the insurance area and discusses financial engineering applications in insurance. There are some key differences between the nature of the risks found in insurance products and those typically found in banking applications. Historically insurance risks were handled using the actuarial approach and we describe this approach and contrast it with the financial engineering approach. We focus on life insurance applications. Life insurance products often include a variety of investment options which are related to the performance of a stock portfolio or an index portfolio. The pricing and risk management of these contracts has provided a challenge to traditional actuarial techniques. In this chapter we describe how the modern approach to risk management combines concepts from modern financial economics and econometrics with ideas from the traditional actuarial approach. We discuss two specific applications: variable annuity contracts and guaranteed annuity options.