The authors study the following problem: Given \(t\) and a stochastic process \(X\) one wants to find a good predictor of \(\Phi(X_ T)\) based on the information \(F^ X_ t\), where \(\Phi\) is a function and \(T>t\). They introduce the notion of a prediction sufficiency. They show that if \(f(t,X_ t)\) is a prediction sufficient process with some optimality properties, then \(f(t,X_ t)\) is a reverse martingale with respect to the filtration \(G_ t^ X=\sigma\{X_ s:s\geq t\}\). The authors compute the optimal predictor in some examples (diffusion processes, Poisson processes) and give explanations for the irregular behaviour of the optimal predictor in these examples. They finish the paper by giving some information inequalities.