This dissertation is concerned with travel time uncertainty in transportation networks due to ephemeral phenomena such as incidents or poor weather. Such events play a major role in nonrecurring congestion, which is estimated to comprise between one-third and one-half of all delay on freeways. Although past research has considered many individual aspects of this problem, this dissertation is unique in bringing a comprehensive approach, beginning with study of its causes, moving to discussion of its effects on traveler behavior, and then demonstrating how these models can be applied to mitigate the effects of this uncertainty. In particular, two distinctive effects of uncertainty are incorporated into all aspects of these models: nonlinear traveler behavior, encompassing risk aversion, schedule delay, on-time arrival, and other user objectives that explicitly recognize travel time uncertainty; and information and adaptive routing, where travelers can adjust their routes through the network as they acquire information on its condition. In order to accurately represent uncertain events in a mathematical model, some quantitative description of these events and their impacts must be available. On freeways, a large amount of travel data is collected through intelligent transportation systems (ITS), although coverage is far from universal, and very little data is collected on arterial streets. This dissertation develops a statistical procedure for estimating probability distributions on speed, capacity, and other operational metrics by applying regression to locations where such data is available. On arterials, queueing theory is used to develop novel expressions for expected delay conditional on the signal indication. The effects of this uncertainty are considered next, both at the individual (route choice) and collective (equilibrium) levels. For individuals, the optimal strategy is no longer a path, but an adaptive policy which allows for flexible re-routing as information is acquired. Dynamic programming provides an efficient solution to this problem. Issues related to cycling in optimal policies are examined in some depth. While primarily a technical concern, the presence of cycling can be discomforting and needs to be addressed. When considering collective behavior, the simultaneous choices of many self-optimizing users (who need not share the same behavioral objective) can be expressed as the solution to a variational inequality problem, leading to existence and uniqueness results under certain regularity conditions. An improved policy loading algorithm is also provided for the case of linear traveler behavior. Finally, three network improvement strategies are considered: locating information-providing devices; adaptive congestion pricing; and network design. Each of these demonstrates how the routing and equilibrium models can be applied, using small networks as testbed locations. In particular, the information provision and adaptive congestion pricing strategies are extremely difficult to represent without an adaptive equilibrium model such as the one provided in this dissertation. / text