We propose new expectation–maximization algorithms to analyze current status data under two popular semiparametric regression models: the proportional hazards (PH) model and the proportional odds (PO) model. Monotone splines are used to model the baseline cumulative hazard function in the PH model and the baseline odds function in the PO model. The proposed algorithms are derived by exploiting a data augmentation based on Poisson latent variables. Unlike previous regression work with current status data, our PH and PO model fitting methods are fast, flexible, easy to implement, and provide variance estimates in closed form. These techniques are evaluated using simulation and are illustrated using uterine fibroid data from a prospective cohort study on early pregnancy. Copyright © 2013 John Wiley & Sons, Ltd.