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.