This chapter considers some of the mathematical properties of the exponential distribution, and this information gives some indication as to the types of variables which may be expected to follow the exponential distribution. The constant hazard function means that the exponential distribution is an appropriate model for the lifetime of an item when there is no wear-out or aging. The no-memory property and other aspects of the exponential distribution make it a particularly convenient model for certain types of problems. The exponential distribution is of practical importance because of its simplicity, and of theoretical importance because it is the breakover point between increasing-failure-rate models and decreasing-failure-rate models. If the cause of failure follows the Poisson process, then the "waiting times" between occurrences follow the exponential distribution. The chapter describes statistical procedures for the one-parameter exponential model based on complete samples.