Truly understanding a scene involves integrating information at multiple levels as well as studying the interactions between scene elements. Individual object detectors, layout estimators and scene classifiers are powerful but ultimately confounded by complicated real-world scenes with high variability, different viewpoints and occlusions. We propose a method that can automatically learn the interactions among scene elements and apply them to the holistic understanding of indoor scenes from a single image. This interpretation is performed within a hierarchical interaction model which describes an image by a parse graph, thereby fusing together object detection, layout estimation and scene classification. At the root of the parse graph is the scene type and layout while the leaves are the individual detections of objects. In between is the core of the system, our 3D Geometric Phrases (3DGP). We conduct extensive experimental evaluations on single image 3D scene understanding using both 2D and 3D metrics. The results demonstrate that our model with 3DGPs can provide robust estimation of scene type, 3D space, and 3D objects by leveraging the contextual relationships among the visual elements.