AbstractThe basic Weibull distribution is considered the most fundamental and basic lifetime distribution. Various extensions of the Weibull distribution have been proposed since the 1970s and are useful in the modeling of complex lifetime data that are beyond the capability of the basic Weibull. This article reviews the properties of the basic Weibull distribution and lists the various extensions. It describes the use of Weibull probability plots as a tool for model selection and discusses the parameter estimation and model validation. It concludes with some topics for future research. WIREs Comp Stat 2011 3 282–287 DOI: 10.1002/wics.157This article is categorized under: Statistical Models > Model Selection