The traffic theorist of today has an ever-increasing capacity to bring a wide range of technical skills to bear on the pressing problems of traffic congestion, delays, and accidents with their ensuing economic and personal costs. These problems are very complex, but well-defined aspects of them can be dealt with theoretically in explicit mathematical form. Illustrations are given as to how this may be done in meaningful ways to find the relationships between important variables and to determine the influence of parameter values on the performance of traffic systems. The problems discussed consider traffic flow in single and multiple lanes, interference between vehicles and queue formations, single and multiple intersection flows and control and road networks.