We develop stochastic models of time-dependent arrivals, with focus on the application to call centers. Our models reproduce essential features of call center arrivals observed in recent empirical studies, namely, a time-varying arrival intensity over the course of a day, and nonzero correlation between the arrival counts in different time periods within the same day. For each of the new models, we characterize the joint distribution of the vector of arrival counts with particular focus on characterizing how the new models are more flexible than standard or previously proposed models. We report empirical results from a study on arrival data from a real-life call center, including the essential features of the arrival process, the goodness-of-fit of the estimated models, and the sensitivity of various simulated performance measures of the call center to the choice of arrival process model.