Survival plots of time-to-event data are a key component for reporting results of many clinical trials (and cohort studies). However, mistakes and distortions often arise in the display and interpretation of survival plots. This article aims to highlight such pitfalls and provide recommendations for future practice. Findings are illustrated by topical examples and also based on a survey of recent clinical trial publications in four major journals. Specific issues are: should plots go up or down (we recommend up), how far in time to extend the plot, showing the extent of follow-up, displaying statistical uncertainty by including SEs or CIS, and exercising caution when interpreting the shape of plots and the time-pattern of treatment difference.