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▼a Knowing the dynamic of a network is essential for society and the economy. Building the correct model of it can help people predict the future and manage the system in advance. This dissertation focuses on modeling opinion and risk dynamic, understanding their temporal and spatial evolution and provide an optimal solution for control and management.Public opinion has a critical impact on society in many aspects, such as election and legislative votes. Thus, it is worth to study the opinion diffusion in a social network. One big challenge of this study is that people's holding opinions are mutually influencing each over about those opinions over time. Hence, we need a networked model to measure the process of opinion diffusion during people's interactions. One of the well-studied models is the Naming Game. The advantage of the model is that after sufficient interactions, the system can achieve a consensus to one opinion. Besides, the final consensus state changes with different initial opinions, network topology, and also changes with a fraction of committed agents in a committed version of the model. To study the phase transition of system states, we propose two extended models, waning and increasing commitment, in which a node will lose or gain commitment to an opinion with a commitment strength, w. We provide the analytical solution of the tipping point of the phase transition, which is an exponential function of w. Further, a system with distributed commitment strengths increases the tipping point value for waning commitment and decrease this value for increasing commitment. With an understanding of the rules of opinion diffusion in a social network, we have an insight into the current public opinions of the system and can predict their future ones.Comparing to opinion dynamic, the analysis of global risk dynamic is wider applicable not only to societal problems but also to economic, environmental, geopolitical, and technological tasks. The global risks are impactful and may cause tremendous damages to humanity, such as economic crisis, natural disaster, and interstate war. Besides, the risks are not isolated. One risk may lead to the activation of another risk and eventually results in risk cascading failure. More importantly, the risks and their propagation network continually evolve. Every year, the World Economic Forum publishes a report of global risks including their definitions, categories, likelihoods to be active, impacts when active and contagious network. Thus, the study of global risk network and its evolution is urgently needed. With the understanding of the principles of risk cascading over time, we can monitor and control the current risks to prevent disasters in the future. Therefore, we introduce Cascading Alternating Renewal Process (CARP) to model the risk cascading and to build yearly models according to annual global risk reports and collected historical data. With the simulated results using the CARP model for each year network, we quantitatively capture the decrease of economic risks since 2014, the regular occurrence of environmental risks, and the increase of societal and technological risks since 2015. In addition to the temporal evolution, the spatial characteristics of risks, which is critical to regional, national, or even global governance, was included in our study. After analyzing the regional risks from Wiki events data, we found periodic economic risks in Europe, regular environmental risks in coastal areas, chronic geopolitical risks in the Middle East, and rising societal risks in East Asia. Furthermore, to better understand the risks from Wiki events and save time of human labeling, we built a risk detection tool that automatically discovers potential risks from event sentences.Beyond knowing the yearly evolution and regional effect of risks, we study a more interesting and challenging question that is how to manage those risks at our desire. This problem can be formulated as network control with a desired final state and optimizer. Although control engineering has been widely researched in complex networks recently, few studies can be directly implemented in global risk network for the following reasons: 1. the intermediate state costs in the risk network are non-negligible |