Lifetime (ageing) distributions play a fundamental role in reliability. We present a semi-unified approach in constructing them, and show that most of the existing distributions may arise from one of these methods. Generalizations/modifications of the Weibull distribution are often required to prescribe the nonmonotonic nature of the empirical hazard rates. We also briefly outline some of the known applications of lifetime distributions in diverse disciplines. Copyright © 2012 John Wiley & Sons, Ltd.