This monograph is, as far as the authors have gathered, the first one of its kind which presents various characterisations of many important and continuous distributions. It consists of six chapters. The first chapter lists cumulative distribution functions, probability density functions, hazard functions and reverse hazard functions of one hundred thirty-six important univariate continuous distributions. Chapter Two provides characterisations of these distributions based on the ratio of two truncated moments. Chapter Three takes up the characterisations of some of these distributions in terms of their hazard functions. Chapter Four deals with the characterisations of some of these distributions based on their reverse hazard functions. Characterisations of some of these distributions based on the conditional expectations of certain functions of the random variable are presented in Chapter Five. Finally, to make this book self-contained, we present the characterisations of a large number of distributions (without their proofs) that have already been published by Hamedani and coauthors in Chapter Six.