This monograph contains a critical review of 50 years of results on questions of admissibility and minimaxity of estimators of parameters that are restricted to closed convex subsets of Rk . It presents results of approximately 300 mostly-published papers on the subject, and points out relationships between them as well as open problems. The book does not touch on the subject of testing hypotheses for such parameter spaces. It does give an overview of known algorithms for computing maximum likelihood estimators under order-restrictions. The book should be valuable as a reference for researchers and graduate students looking for what is known and unknown in the area of restricted parameter-space-estimation. It assumes a good knowledge of decision theory.