In dose-finding trials, it is desirable to make dose assignment decisions in real time in the presence of pending toxicity outcomes, especially when patient accrual is fast or the dose limiting toxicity is of late-onset. Several time-to-event designs have been proposed for this purpose by utilizing the follow-up time information. We present a unified statistical framework for time-to-event designs to reveal the connection among the existing methods. The general idea is to treat the pending outcomes as censored observations or missing data and proceed with inference by modeling the time-to-toxicity. The frame- work opens the door to new designs, including a class of designs based on probabilistic rules of dose-finding decisions. To facilitate the use of time-to-event designs in practice, we introduce efficient computational algorithms and review common practical considerations such as safety rules and suspension rules. Large sample convergence properties of interval-based time-to-event designs are studied in theory. Finally, the operating characteristics of several designs are evaluated and compared through computer simulations.