There is a popular perception that man-made global warming is causing sea levels to rise dramatically. However, while some computer models have made fairly dramatic predictions, and Hollywood has exaggerated these into completely implausible scenarios to make entertaining science fiction, the actual experimental data fails to show anything dramatic. Instead, it suggests a sea level rise of at most a few inches per century. But, even those modest estimates are likely to be too large, as they neglect a number of serious biases in the data. In this essay, we analyse the actual data.