Surface depressions are one of the significant topographic characteristics in depression-dominated areas and can retain runoff and break the hydrologic continuity in watersheds. In traditional semi-distributed models, the entire area of a watershed is assumed to be well connected to its associated outlet and depressions are often lumped as a single depth to control runoff water release. Consequently, hydrologic processes related to depressions cannot be directly simulated. The overall goal of this dissertation research is to analyze and quantify the topographic characteristics of surface depressions and their impacts on hydrologic processes in depression-dominated areas. The specific objectives of this research are: (1) to improve watershed delineation to further reveal the topographic characteristics and hydrologic connectivity within watersheds, (2) to analyze the impact of depressions on runoff processes during rainfall events and the mechanism of water release from depressions, and (3) to analyze the functionalities of depressions in continuous simulation of hydrologic processes and connectivity. A new algorithm was developed for hydrologic unit delineation of depressions and channels (HUD-DC), in which a unique method was proposed to identify depression- and channel-associated hydrologic units and their connections. The HUD-DC delineation results highlighted the significance of depressions and the complex connectivity in depression-dominated areas. Additionally, the delineation under different filling conditions provided helpful guidance for the identification of filling thresholds to remove artifacts in digital elevation models. To achieve the second objective, a depression-oriented, event-based hydrologic model (HYDROL-D) was developed with considering separate modeling for depressional and non-depressional areas, and hierarchical control thresholds for water release from depressions. The HYDROL-D modeling results for a watershed in North Dakota revealed the intrinsic threshold behavior of surface runoff over the watershed and the effectiveness of the hierarchical control thresholds. A depression-oriented hydrologic model with accounting for dynamic hydrologic connectivity (HYDROL-DC) was further developed to continuously track runoff unit by unit. The application of HYDROL-DC in a depression-dominated watershed showed that depressions had not only retention but also acceleration capabilities in surface runoff generation. Additionally, the spatial distribution of depressions exhibited dynamic influences on hydrologic connectivity and the related threshold behavior of runoff processes.