The paper reviews the principles of financial intermediation in insurance from the perspective of its functions in the financial system and assesses the effect of financial innovation on insurance functions. Insurance core function is managing risks driven by nature or related to human life. To support it, insurance companies perform the functions of pooling of resources, transferring of resources, and information production and management. Four major financial innovations affected the insurance business: hedging of market risks with derivatives, securitization of underwriting risks, asset management and credit intermediation activities of the shadow banking. While hedging of market risks with derivatives and securitization of underwriting risks enhanced industry effectiveness to perform its core functions, asset management and shadow banking activities introduced new functions of supporting the payment system and asset prices. In performing new functions, insurers compete with other financial intermediaries and markets. The analysis implies that an economic activity rather than a legal entity needs to be the basis of systemic risk regulation framework in insurance. This would also provide a coherent framework to regulate various intermediaries involved in economically equivalent activities.