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The physical processes that shape landscapes are complex and involve the interaction of water, soil, vegetation and biota over a range of scales. Yet, as complex as these interactions may seem to be, the landscapes we see around us often exhibit striking hierarchical order and geometric/statistical properties that are subject to scale renormalization. The overall goal of this research is to contribute to the theoretical foundation of extracting geomorphic features of interest from high resolution topography and use the extracted features for process understanding and for advancing landscape evolution modeling. Specifically, an advanced methodology for geomorphic feature extraction is developed and implemented on several high resolution data sets of different characteristics, from a steep and landslide-dissected basin, to a mountainous region, to a flat and partly artificially drained area. This new methodology incorporates nonlinear diffusion for the pre-processing of the data, both to focus the analysis on the scales of interest and to enhance features that are critical to the network extraction. Following this pre-processing, channels are defined as curves of minimal effort, or geodesics, where the effort is measured based on fundamental geomorphological characteristics such as flow accumulation and iso-height contours curvature. The developed channel network extraction methodology is compared in terms of performance to a previously proposed channel extraction methodology based on wavelets. The results show that the geometric nonlinear framework is more computationally efficient and achieves better localization and robust extraction of features, especially in areas where gentle slopes prevail. The automatic extraction of channel morphology, such as cross-section, banks location, water surface elevation, is also addressed, as well as the possibility of distinguishing the signature of natural features such as channels from the one of artificial features, such as drainage ditches. One motivation for extracting detailed geomorphic features from landscapes is the premise that this will lead to improved process understanding (e.g., by relating the observed form to physical processes that gave rise to that form) and improved modeling (e.g., incorporate important localized features in hydrologic or sediment transport models or develop sophisticated metrics for testing the performance of landscape evolution models). With this premise in mind, work herein presents preliminary results along a particular new direction related to geomorphic transport laws and landscape evolution modeling. Specifically, motivated by: (a) our experience that geomorphic attributes, such as slope and curvature, are scale-dependent and thus the resulting sediment flux computed from the typical transport laws would also be scale-dependent, and (b) that landscapes present heterogeneity over a large range of scales, we put forward the idea of a non-local sediment flux formulation to be explored in landscape evolution modeling. Along these lines, a simple landscape evolution model is proposed and its ability to reproduce some common statistical properties of real landscapes is examined.