The two-parameter Weibull distribution is the most popular model for material strength. However, it may not be a good model for all materials over a wide range of sizes. In this note, a comprehensive review of the known variations of the two-parameter Weibull distribution is provided to help providing better modeling. Over 20 variations are reviewed. The appropriateness of the variations is discussed as models for brittle versus ductile strength. A comparison study of a selection of the variations is also provided. It is hoped that this review will also serve as an important reference and encourage developments of further variations of the two-parameter Weibull distribution.