Embedded within the regression framework, local models can estimate conditioned relationships between observed spatial phenomena and hypothesized explanatory variables and help infer the intangible spatial processes that contribute to the observed spatial patterns. Rather than investigating averaged characteristics corresponding to processes over space as global models do, these models estimate a surface of spatially varying parameters with a value for each location. Additionally, some models such as variants within the Geographically Weighted Regression (GWR) framework, also estimate a parameter to represent the spatial scale across which the processes vary representing the inherent heterogeneity of the estimated surfaces. Since different processes tend to operate at unique spatial scales, some extensions to local models such as Multiscale GWR (MGWR) estimate unique scales of association for each predictor in a model and generate significantly more information on the nature of geographic processes than their predecessors. However, developments within the realm of local models are fairly nascent and hence an understanding around their correct application as well as recognizing their true potential in exploring fundamental spatial science issues is under-developed. The techniques within these frameworks are also currently limited thus restricting the kinds of data that can be analyzed using these models. Therefore the goal of this dissertation is to advance techniques within local multiscale modeling specifically by coining new diagnostics, exploring their novel application in understanding long-standing issues concerning spatial scale and by expanding the tool base to allow their use in wider empirical applications. This goal is realized through three distinct research objectives over four chapters, followed by a discussion on the future of the developments within local multiscale modeling. A correct understanding of the capability and promise of local multiscale models and expanding the fields where they can be employed will not only enhance geographical research by strengthening the intuition of the nature of geographic processes, but will also exemplify the importance and need for using such tools bringing quantitative spatial science to the fore.