As an important endogenous source of reactive oxygen species (ROS), NADPH oxidase 1 (Nox1) has received tremendous attention in the past few decades. It has been identified to play a key role as the initial "kindle," whose activation is crucial for amplifying ROS production through several propagation mechanisms in the vascular system. As a consequence, Nox1 has been implicated in the initiation and genesis of many cardiovascular diseases and has therefore been the subject of detailed investigations. The literature on experimental studies of the Nox1 system is extensive. Numerous investigations have identified essential features of the Nox1 system in vasculature and characterized key components, possible regulatory signals and/or signaling pathways, potential activation mechanisms, a variety of Nox1 stimuli, and its potential physiological and pathophysiological functions. While these experimental studies have greatly enhanced our understanding of the Nox1 system, many open questions remain regarding the overall functionality and dynamic behavior of Nox1 in response to specific stimuli. Such questions include the following. What are the main regulatory and/or activation mechanisms of Nox1 systems in different types of vascular cells? Once Nox1 is activated, how does the system return to its original, unstimulated state, and how will its subunits be recycled? What are the potential disassembly pathways of Nox1? Are these pathways equally important for effectively reutilizing Nox1 subunits? How does Nox1 activity change in response to dynamic signals? Are there generic features or principles within the Nox1 system that permit optimal performance? These types of questions have not been answered by experiments, and they are indeed quite difficult to address with experiments. I demonstrate in this dissertation that one can pose such questions and at least partially answer them with mathematical and computational methods. Two specific cell types, namely endothelial cells (ECs) and vascular smooth muscle cells (VSMCs), are used as "templates" to investigate distinct modes of regulation of Nox1 in different vascular cells. By using a diverse array of modeling methods and computer simulations, this research identifies different types of regulation and their distinct roles in the activation process of Nox1. In the first study, I analyze ECs stimulated by mechanical stimuli, namely shear stresses of different types. The second study uses different analytical and simulation methods to reveal generic features of alternative disassembly mechanisms of Nox1 in VSMCs. This study leads to predictions of the overall dynamic behavior of the Nox1 system in VSMCs as it responds to extracellular stimuli, such as the hormone angiotensin II. The studies and investigations presented here improve our current understanding of the Nox1 system in the vascular system and might help us to develop potential strategies for manipulation and controlling Nox1 activity, which in turn will benefit future experimental and clinical studies.