In this thesis, we present two new paradigms for yield-stress fluids; the first organizes the existing understanding of the various ways to achieve a yield-stress fluid into a useful methodology for the design of rheologically complex materials; the second is based on the discrepancy in the behavior in extension of model yield-stress fluids versus application-relevant materials. Through implementation of material design principles of selection and synthesis, yield-stress fluid microstructures are organized according to the two known mechanical interactions capable of producing them (jamming and attraction). This rheology-to-structure inverse problem reveals trade-offs in designing yield-stress fluids, demonstrating that multiple material classes can achieve a target yield stress, providing the opportunity for creative design to achieve both the yield stress and other secondary design criteria. A secondary design criteria that is investigated in depth here is extensibility. We introduce a method for characterizing the extensibility of yield-stress fluids, demonstrate the extent to which existing model materials differ from the high extensibility seen in real yield-stress fluids (commercial products, biomaterials), and introduce an attempt at creating a model material for highly-extensible yield-stress fluids.