Order-restricted inference is a fertile area of research; structures involving orderings and inequalities increase the efficiency of statistical inference procedures, and are easy to interpret and apply. This book presents recent developments in statistical inference subject to inequality constraints, concentrating on procedures based on the likelihood principle. Using as a model the influential Statistical Inference under Order Restrictions, by Barlow et al. (1972), the authors present the latest results on isotonic regression, tests of ordered hypotheses (the normal means case), the increasing use of duality, and much more. Contains over 800 references.