In statistical mechanics, the term “quenched disorder” refers to heterogeneity that is fixed, unable to respond to changes in a material. Thermal fluctuations and quenched disorder are two distinct types of randomness that can control the statistical mechanics of condensed matter. In soft materials, thermal fluctuations usually dominate because heterogeneities are free to move around a sample. However, recent research has found certain types of soft materials where quenched disorder plays the dominant role. In this talk, we present theoretical models for two such systems. For helical polymers, including polyisocyanates and DNA, we show that the helical order of the chains is controlled by the disordered sequence of monomer units. For liquid-crystalline elastomers, we show that the sharpness of the isotropic-nematic transition is controlled by heterogeneity in the crosslinked polymer network. In both cases, statistical models can explain experimental results and make predictions for future experiments with potential technological applications.