We study inference on parameters in censored panel data models, where the censoring can depend on both observable and unobservable variables in arbitrary ways. Under some general conditions, we characterize the information the model and data contain about the parameters of interest by deriving the identified sets: Every parameter that belongs to these sets is observationally equivalent to the true parameter - the one that generated the data . We consider two separate sets of assumptions (2 models): the first uses stationarity on the unobserved disturbance terms. The second is a nonstationary model with a conditional independence restriction. Based on the characterizations of the identified sets, we provide a valid inference procedure that is shown to yield correct confidence sets based on inverting stochastic dominance tests. Also, we also show how our results extend to empirically interesting dynamic versions of the model with both lagged observed outcomes, and lagged indicators. We also show extensions to models with factor loads. In addition, and for both models, we provide sufficient conditions for point identification in terms of support conditions. The paper then examines sizes of the identified sets, and a Monte Carlo exercise shows reasonable small sample performance of our procedures.