After decades of development and use in a variety of application areas, Quantitative Structure Property Relationships (QSPRs) and related descriptor-based statistical learning methods have achieved a level of infamy due to their misuse. The field is rife with past examples of overtrained models, overoptimistic performance assessment, and outright cheating in the form of explicitly removing data to fit models. These actions do not serve the community well, nor are they beneficial to future predictions based on established models. In practice, in order to select combinations of descriptors and machine learning methods that might work best, one must consider the nature and size of the training and test datasets, be aware of existing hypotheses about the data, and resist the temptation to bias structure representation and modeling to explicitly fit the hypotheses. The definition and application of these best practices is important for obtaining actionable modeling outcomes, and for setting user expectations of modeling accuracy when predicting the endpoint values of unknowns. A wide variety of statistical learning approaches, descriptor types, and model validation strategies are explored herein, with the goals of helping end users understand the factors involved in creating and using QSPR models effectively, and to better understand relationships within the data, especially by looking at the problem space from multiple perspectives. Molecular relationships are commonly envisioned in a continuous high-dimensional space of numerical descriptors, referred to as chemistry space. Descriptor and similarity metric choice influence the partitioning of this space into regions corresponding to local structural similarity. These regions, known as domains of applicability, are most likely to be successfully modeled by a QSPR. In Chapter 2, the network topology and scaling relationships of several chemistry spaces are thoroughly investigated. Chemistry spaces studied include the ZINC data set, a qHTS PubChem bioassay, as well as the protein binding sites from the PDB. The characteristics of these networks are compared and contrasted with those of the bioassay Structure Activity Landscape Index (SALI) subnetwork, which maps discontinuities or cliffs in the structure activity landscape. Mapping this newly generated information over underlying chemistry space networks generated using different descriptors demonstrates local modeling capacity and can guide the choice of better local representations of chemistry space. Chapter 2 introduces and demonstrates this novel concept, which also enables future work in visualization and interpretation of chemical spaces. Initially, it was discovered that there were no community-available tools to leverage best-practice ideas to comprehensively build, compare, and interpret QSPRs. The Yet Another Modeling System (YAMS) tool performs a series of balanced, rational decisions in dataset preprocessing and parameter/feature selection over a choice of modeling methods. To date, YAMS is the only community-available informatics tool that performs such decisions consistently between methods while also providing multiple model performance comparisons and detailed descriptor importance information. The focus of the tool is thus to convey rich information about model quality and predictions that help to "close the loop" between modeling and experimental efforts, for example, in tailoring nanocomposite properties. Polymer nanocomposites (PNC) are complex material systems encompassing many potential structures, chemistries, and self assembled morphologies that could significantly impact commercial and military applications. There is a strong desire to characterize and understand the tradespace of nanocomposites, to identify the important factors relating nanostructure to materials properties and determine an effective way to control materials properties at the manufacturing scale. Due to the complexity of the systems, existing design approaches rely heavily on trial-and-error learning. By leveraging existing experimental data, Materials Quantitative Structure-Property Relationships (MQSPRs) relate molecular structures to the polar and dispersive components of corresponding surface tensions. In turn, existing theories relate polymer and nanofiller polar and dispersive surface tension components to the dispersion state and interfacial polymer relaxation times. These quantities may, in the future, be used as input to continuum mechanics approaches shown able to predict the thermomechanical response of nanocomposites. For a polymer dataset and a particle dataset, multiple structural representations and descriptor sets are benchmarked, including a set of high performance surface-property descriptors developed as part of this work. The systematic variation of structural representations as part of the informatics approach reveals important insight in modeling polymers, and should become common practice when defining new problem spaces. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]