Amorphous (non-crystalline) materials offer new capabilities and applications relative to their corresponding crystalline phases due to their novel and tunable material properties, including but not limited to larger surface area, wider substrate compatibility, stronger corrosion resistance, and lower temperature processing than their crystal counterparts. However, even the most advanced experimental techniques (e.g., in situ NMR and ``inverse" approaches such as Reverse Monte Carlo (RMC) modeling of diffraction data) cannot directly measure the bulk atomic structure of such complex, non-crystalline materials. This, coupled with the lack of a structural theory of amorphous materials, has limited our understanding about the structure-property relationships required for the optimization of realistic devices. In this thesis, we compare and combine several atomistic modeling techniques for generating accurate and general structures of amorphous systems, both solid and liquid. We develop several metrics for measuring efficiency of configuration space sampling to guide and standardize the computational study of amorphous materials, and use these to differentiate between different samples of amorphous structures. Lastly, we use these structures to help elucidate structure-property relationships in these systems. In amorphous metal oxides, we characterize the types of coordination defects in amorphous metal oxide systems and subsequently identify potential electron and hole traps in their electronic structures. In a liquid system, water-in-salt electrolytes, we evaluate how the hydrogen bonding network and ion coordination shells change with composition, and how these are directly correlated to battery performance.