When dealing with missing responses, two types of omissions can be discerned: items can be skipped or not reached by the test taker. When the occurrence of these omissions is related to the proficiency process the missingness is nonignorable. The purpose of this article is to present a tree-based IRT framework for modeling responses and omissions jointly, taking into account that test takers as well as items can contribute to the two types of omissions. The proposed framework covers several existing models for missing responses, and many IRTree models can be estimated using standard statistical software. Further, simulated data is used to show that ignoring missing responses is less robust than often considered. Finally, as an illustration of its applicability, the IRTree approach is applied to data from the 2009 PISA reading assessment.