Surrogate endpoints offer the hope of smaller or shorter cancer trials. It is, however, important to realize they come at the cost of an unverifiable extrapolation that could lead to misleading conclusions. With cancer prevention, the focus is on hypothesis testing in small surrogate endpoint trials before deciding whether to proceed to a large prevention trial. However, it is not generally appreciated that a small surrogate endpoint trial is highly sensitive to a deviation from the key Prentice criterion needed for the hypothesis-testing extrapolation. With cancer treatment, the focus is on estimation using historical trials with both surrogate and true endpoints to predict treatment effect based on the surrogate endpoint in a new trial. Successively leaving out one historical trial and computing the predicted treatment effect in the left-out trial yields a standard error multiplier that summarizes the increased uncertainty in estimation extrapolation. If this increased uncertainty is acceptable, three additional extrapolation issues (biological mechanism, treatment following observation of the surrogate endpoint, and side effects following observation of the surrogate endpoint) need to be considered. In summary, when using surrogate endpoint analyses, an appreciation of the problems of extrapolation is crucial.