Book excerpt: The Weibull distribution has been one of the most cited lifetime distributions in reliability engineering. Over the last decade, many generalizations and extensions of the Weibull have been proposed in order to provide more flexibility than the traditional version when it comes to modeling lifetime data in diverse fields. This book offers an update on these developments, presenting the essential properties of each model. Several plots of density and hazard rate functions are also included, and a brief outline of known application(s) for each model is also given. ​