We analyze the relationship between asset price bubbles and systemic risk, using bank-level data covering almost thirty years. Systemic risk of banks rises already during a bubble's build-up phase, and even more so during its bust. The increase differs strongly across banks and bubble episodes. It depends on bank characteristics (especially bank size) and bubble characteristics, and it can become very large: In a median real estate bust, systemic risk increases by almost 70~percent of the median for banks with unfavorable characteristics. These results emphasize the importance of bank-level factors for the build-up of financial fragility during bubble episodes.