There has recently been a lot of interest in developing approaches to handle missing data that go beyond the traditional assumptions of the missing data being missing at random and the nonresponse mechanism being ignorable. Of particular interest are approaches that have the property of being nonparametric identified, because these approaches do not impose parametric restrictions on the observed-data distribution (what we can estimate from the observed data) while allowing estimation under a full-data distribution. When comparing inferences obtained from different nonparametric identified approaches, we can be sure that any discrepancies are the result of the different identifying assumptions imposed on the parts of the full-data distribution that cannot be estimated from the observed data, and consequently these approaches are especially useful for sensitivity analyses. In this talk I will present some recent developments in this area of research and discuss current challenges.