In various banking models, banks are viewed as arrangements that insure households against uncertain liquidity needs. However, the exact nature of the liquidity risk faced by households – and hence the insurance function of banks – differs across models. This paper attempts to disentangle the different meanings of the term ‘liquidity insurance’ in the literature and to clarify what kind of insurance banks provide in which models. The paper also shows under which conditions banking is equivalent to eliminating uncertainty about liquidity needs or letting households trade with each other in an asset market. Special attention is given to the comparison of banking models in the tradition of Diamond and Dybvig (1983) with those based on monetary (notably New Monetarist) frameworks.