This chapter considers interval estimation of a single parameter and region estimation of a vector of parameters. The Bayesian decision theoretic approach considers the choice of a particular interval or region for an unknown parameter as a decision-making problem. The empirical Bayes approach aims at obtaining estimates of the Bayes regions which converge to the true Bayes regions when the amount of previous data increases. With respect to data sets in the typical Empirical Bayes (EB) sampling scheme the EB regions are random. The earliest development of an EB interval estimate seems to be due to J. J. Deely and W. J. Zimmer although the first use of the term ' EB interval estimate' appears to be by D. R. Cox. C. N. Morris gives an EB interval estimation technique. Although the sampling properties of the intervals are of main interest, the method is similar to the Bayes EB method.