In today's world, unprecedented amounts of data of individual mobile objects have become more available due to advances in location aware technologies and services. Studying the spatio-temporal patterns, processes, and behavior of mobile objects is an important issue for extracting useful information and knowledge about mobile phenomena. Potential applications across a wide range of fields include urban and transportation planning, Location-Based Services, and logistics. This research is designed to contribute to the existing state-of-the-art in tracking and modeling mobile objects, specifically targeting three challenges in investigating spatio-temporal patterns and processes; 1) a lack of space-time analysis tools; 2) a lack of studies about empirical data analysis and context awareness of mobile objects; and 3) a lack of studies about how to evaluate and test agent-based models of complex mobile phenomena. Three studies are proposed to investigate these challenges; the first study develops an integrated data analysis toolkit for exploration of spatio-temporal patterns and processes of mobile objects; the second study investigates two movement behaviors, 1) theoretical random walks and 2) human movements in urban space collected by GPS; and, the third study contributes to the research challenge of evaluating the form and fit of Agent-Based Models of human movement in urban space. The main contribution of this work is the conceptualization and implementation of a Geographic Knowledge Discovery approach for extracting high-level knowledge from low-level datasets about mobile objects. This allows better understanding of space-time patterns and processes of mobile objects by revealing their complex movement behaviors, interactions, and collective behaviors. In detail, this research proposes a novel analytical framework that integrates time geography, trajectory data mining, and 3D volume visualization. In addition, a toolkit that utilizes the framework is developed and used for investigating theoretical and empirical datasets about mobile objects. The results showed that the framework and the toolkit demonstrate a great capability to identify and visualize clusters of various movement behaviors in space and time.