This chapter addresses the Kumaraswamy's generalized (\Kw-G" for short) family of models. A physical motivation for the Kw-G family is presented and some of its special cases are discussed in detail. This family receives a baseline distribution as input and returns a new distribution with two additional parameters. The returned model is often more exible than the baseline one. Several structural properties are presented and discussed for the Kw-G family. Among them, useful expansions, mgf, moments and mean deviations. Additionally, estimation and generation procedures are presented.