Statistical distributions are fundamental to statistical science and are a prime indispensable tool for its applications. This monograph is the first to examine an important but somewhat neglected area in this field -- univariate continuous distributions on a bounded domain, excluding the beta distribution. It provides an elementary but thorough discussion of "novel" contributions developed in recent years and some of their applications. It contains a comprehensive chapter on the triangular distribution as well as a chapter on earlier extensions of this distribution not emphasized in existing statistical literature. Special attention is given to estimation, in particular, non-standard maximum likelihood procedures.