We develop new representations and algorithms for three-dimensional (3D) object detection and spatial layout prediction in cluttered indoor scenes. We first propose a clouds of oriented gradient (COG) descriptor that links the 2D appearance and 3D pose of object categories, and thus accurately models how perspective projection affects perceived image gradients. To better represent the 3D visual styles of large objects and provide contextual cues to improve the detection of small objects, we introduce latent support surfaces. We then propose a "Manhattan voxel" representation which better captures the 3D room layout geometry of common indoor environments. Effective classification rules are learned via a latent structured prediction framework. Contextual relationships among categories and layout are captured via a cascade of classifiers, leading to holistic scene hypotheses that exceed the state-of-the-art on the SUN RGB-D database.