Transportation is a field which is universal in our society: people from every country, culture or background are familiar with the challenges of getting around in our built environment. Yet what is not always so obvious to the average traveler is how the techniques and tools of designing, observing, and controlling our modern transportation networks are derived. In fact, the theory of traffic engineering has many gaps and unknowns that are the topic of ongoing research efforts in the academic community. This work presents a collection of theoretical and practical methodologies to advance the study of traffic flow modeling, state estimation, and control of signalized roadways in particular. It uses theory from traditional transportation engineering, but also demonstrates the application of new tools from control theory and computer science to the specific application of signalized traffic networks. First, two numerical modeling dynamics representing traffic flows on signalized arterials are presented: the well-known Cell Transmission Model, a discretization of the physical hydrodynamic laws believed to govern vehicle flows, and a new Vertical Cell Model which resembles classical "store-and-forward" models with the addition of transit delays and finite buffer capacities. Each of these models is implemented in a common software framework, which provides an ideal experimental platform for direct comparison of the competing dynamics. A chapter in this dissertation contributes a validation and comparison of the two models against real vehicle trajectory data on an existing signalized road network. Accuracy and confidence in such traffic models requires complimentary methods of observing true traffic conditions to provide initial conditions and real-time state estimates. Yet there are many technological deficiencies in existing urban roadway detection systems that prevent the acquisition of a real-time estimate of arterial link state (or queue length) at signalized intersections. Hence this thesis also contains methodology to improve the estimates obtained from existing hardware by combining data from typical infrastructure sensors with new sources of Lagrangian probe measurements. These are then assimilated into a detailed model of flow dynamics. This technique was previously proposed for continuous-flow (freeway) networks, but required novel adaptions to be applied to an interrupted-flow setting. This dissertation next explores advancements in theoretically optimal control algorithms for statistically-modeled signalized queueing networks. In the context of a large body of previous work on flow-impeding control for vertical queueing networks, the practical challenges of traffic signal control are highlighted. Some of these challenges are tackled in the specific case of the max pressure controller, an algorithm derived from the field of communications networks that has been shown to optimize through-flow in an idealized network model. The lack of adequate measurements or demand-volume data has historically been a major limitation in advancing research on signalized arterial road networks. Yet the current revolution of inexpensive storage and processing of "big data" shows promise for improving daily operations of existing roadways without the need for expensive new hardware systems. One example of this potential appears is the case of traffic signal control. Existing traffic signals are capable of operating more efficiently by changing signal plans based on real-time demand measurements through a traffic responsive plan selection (TRPS) mode of operation (rather than depending on a rigid schedule for plan changes). However, this mode is rarely used in practice because its calibration process is not accessible or intuitive to traffic technicians. This dissertation presents an application of statistical learning techniques to improve the process of calibrating and implementing an existing TRPS mechanism. A proof-of-concept implementation using historical sensor data from a busy urban intersection demonstrates that real operational improvements may be immediately achievable using existing sensing infrastructure.