Interval censoring means that an event time is only known to lie in an interval (L,R], with L the last examination time before the event, and R the first after. In the univariate case, parametric models are easily fitted, whereas for non-parametric models, the mass is placed on some intervals, derived from the L and R points. Asymptotic results are simple for the former and complicated for the latter. This paper is a review describing the extension to multivariate data, like eruption times for teeth examined at visits to the dentist. Parametric models extend easily to multivariate data. However, non-parametric models are intrinsically more complicated. It is difficult to derive the intervals with positive mass, and estimated interval probabilities may not be unique. A semi-parametric model makes a compromise, with a parametric model, like a frailty model, for the dependence and a non-parametric model for the marginal distribution. These three models are compared and discussed. Furthermore, extension to regression models is considered. The semi-parametric approach may be sensible in many cases, as it is more flexible than the parametric models, and it avoids some technical difficulties with the non-parametric approach.