This paper analyzes liquidity risk, liquidity creation, and financial fragility in banking. Douglas W. Diamond and Raghuram G. Rajan argue that banks can resolve liquidity problems that arise in direct lending by enabling depositors to withdraw at low cost and buffering firms from the liquidity needs of their investors. Banks have a fragile capital structure, subject to bank runs, which allows them to perform these functions. The authors show that the funding of illiquid loans by a bank with volatile demand deposits is rationalized in the context of the functions it performs. This model can be used to investigate important issues such as narrow banking and bank capital requirements. The paper discusses the role of banks in transforming illiquid assets into more liquid demand deposits. However, there is a fundamental incompatibility between the two activities -- the demands for liquidity by depositors may arrive at an inconvenient time and force the fire-sale liquidation of illiquid assets. Furthermore, because depositors are served in sequence, the prospect of fire sales may precipitate self-fulfilling runs that further jeopardize bank activities. The authors argue that financial fragility is a desirable characteristic of banks, as it allows liquidity creation. The paper presents a framework where entrepreneurs and potential financiers interact. Entrepreneurs have projects that require investment and produce riskless cash flows. Potential financiers have endowments and can raise money by issuing contracts. The paper discusses the concept of relationship lending, where the lender develops specific skills in identifying the liquidation value of the assets. The lender can extract more from the entrepreneur if she has specific skills. The paper also discusses the concept of limited commitment, where financiers cannot commit to work on a specific venture for a specific date. This leads to the possibility of renegotiation. The paper also discusses the concept of liquidity shock, where the lender could get a highly valued investment or consumption opportunity that makes her impatient. The paper shows that the illiquidity premium is the increase in expected payments the entrepreneur has to make over and above the expected payments the lender would receive if she had invested in storage at date 0. The paper concludes that the illiquidity premium is a necessary condition for both the illiquidity of the real asset (the project) and the financial asset (the loan). The source of the illiquidity premium is that the maximum loan sale price, S, is lower than the present value of the amount obtainable by the patient relationship lender. The paper also discusses the role of banks in financial intermediation, where the relationship lender can commit to pass through everything she extracts from the entrepreneur. This allows her to raise up to X2 at date 1 from investors, which is the same as having S = X2. This enables the intermediary to drive the illiquidity premium in the loans she makes to zero.This paper analyzes liquidity risk, liquidity creation, and financial fragility in banking. Douglas W. Diamond and Raghuram G. Rajan argue that banks can resolve liquidity problems that arise in direct lending by enabling depositors to withdraw at low cost and buffering firms from the liquidity needs of their investors. Banks have a fragile capital structure, subject to bank runs, which allows them to perform these functions. The authors show that the funding of illiquid loans by a bank with volatile demand deposits is rationalized in the context of the functions it performs. This model can be used to investigate important issues such as narrow banking and bank capital requirements. The paper discusses the role of banks in transforming illiquid assets into more liquid demand deposits. However, there is a fundamental incompatibility between the two activities -- the demands for liquidity by depositors may arrive at an inconvenient time and force the fire-sale liquidation of illiquid assets. Furthermore, because depositors are served in sequence, the prospect of fire sales may precipitate self-fulfilling runs that further jeopardize bank activities. The authors argue that financial fragility is a desirable characteristic of banks, as it allows liquidity creation. The paper presents a framework where entrepreneurs and potential financiers interact. Entrepreneurs have projects that require investment and produce riskless cash flows. Potential financiers have endowments and can raise money by issuing contracts. The paper discusses the concept of relationship lending, where the lender develops specific skills in identifying the liquidation value of the assets. The lender can extract more from the entrepreneur if she has specific skills. The paper also discusses the concept of limited commitment, where financiers cannot commit to work on a specific venture for a specific date. This leads to the possibility of renegotiation. The paper also discusses the concept of liquidity shock, where the lender could get a highly valued investment or consumption opportunity that makes her impatient. The paper shows that the illiquidity premium is the increase in expected payments the entrepreneur has to make over and above the expected payments the lender would receive if she had invested in storage at date 0. The paper concludes that the illiquidity premium is a necessary condition for both the illiquidity of the real asset (the project) and the financial asset (the loan). The source of the illiquidity premium is that the maximum loan sale price, S, is lower than the present value of the amount obtainable by the patient relationship lender. The paper also discusses the role of banks in financial intermediation, where the relationship lender can commit to pass through everything she extracts from the entrepreneur. This allows her to raise up to X2 at date 1 from investors, which is the same as having S = X2. This enables the intermediary to drive the illiquidity premium in the loans she makes to zero.