Associated with the lifetime of a living or a non-living object (a random variable) and its distribution are the distribution of residual or remaining life at some age (time) t, the equilibrium distribution and the distribution of the failure rate or the reversed failure rate (looked upon as a random function of t, the age or time survived). Linked up with the concept of residual life is that of inactivity time noted at some time t given that the unit had failed prior to t. These distributions and their properties along with inter-relations among the latter have been useful in determining the original life distributions uniquely, in characterizing specific lifetime distributions, in studying ageing properties of such distributions, in classifying life distributions as also in testing for departure of the underlying life distribution from exponentiality or from other class property.