The last couple of decades have seen a large amount of activity in the area of surrogate marker and surrogate endpoint validation, both from a clinical and a statistical perspective. Prentice made a pivotal contribution in the context of a single trial. Subsequently, the framework he proposed has been discussed, criticized, and extended. An important class of extensions considers several rather than a single trial. Recently, a lot of work has been done in this so-called hierarchical or meta-analytic framework. In this paper, we review both the single trial and the hierarchical framework. A number of applications, scattered throughout the literature, are brought together. We outline the statistical issues involved in trying to validate surrogate endpoints. Clearly statistical evidence should only be seen as a component in a decision making process that also involves a number of clinical and biological considerations.