This short monograph provides a synthesis of new research on sampling designs that are dependent on sample moments or the order statistics of auxiliary variables. The range of survey sampling methods and their applications has gradually increased over time, and these applications have led to new theoretical solutions that provide better sampling designs or estimators. Recently, several important properties of sampling designs have been discovered, and many new methods have been published. Offering an overview of these developments, this book describes sampling designs dependent on the sample generalized variance of auxiliary variables, examines properties of sampling designs proportional to functions of sample order statistics of the auxiliary variable, and takes into account continuous sampling designs. The text will be useful for students and statisticians whose work involves survey sampling, and it will inspire those looking for new sampling designs dependent on auxiliary variables.