Four major frameworks have been developed for evaluating surrogate markers in randomized trials: one based on conditional independence of observable variables, another based on direct and indirect effects, a third based on a meta-analysis, and a fourth based on principal stratification. The first two of these fit into a paradigm we call the causal-effects (CE) paradigm, in which, for a good surrogate, the effect of treatment on the surrogate, combined with the effect of the surrogate on the clinical outcome, allow prediction of the effect of the treatment on the clinical outcome. The last two approaches fall into the causal-association (CA) paradigm, in which the effect of the treatment on the surrogate is associated with its effect on the clinical outcome. We consider the CE paradigm first, and consider identifying assumptions and some simple estimation procedures; we then consider the CA paradigm. We examine the relationships among these approaches and associated estimators. We perform a small simulation study to illustrate properties of the various estimators under different scenarios, and conclude with a discussion of the applicability of both paradigms.