Xuegang (Jeff) Ban Rensselaer Polytechnic Institute Dynamic User Equilibrium (DUE) problems are one of the most challenging problems in transportation science. Extensive research has been done in the past on modeling/solving DUE problems, mainly in the discrete-time domain. This talk concerns about modeling and solving DUE in the continuous-time domain, which enables the investigation of some fundamental issues of DUE such as discretization, convergence, etc. By applying a recent mathematical paradigm, named Differential Complementarity Systems (DCS), it is shown that DCS can better capture the key characteristics of continuous-time DUE and allows more rigorous modeling of the problem. Challenges and future research directions of using DCS to model and solve DUE will also be presented.