Planes are predominant features of man-made environments which have been exploited in many mapping approaches. In this paper, we propose a real-time capable RGB-D SLAM system that consistently integrates frame-to-keyframe and frame-to-plane alignment. Our method models the environment with a global plane model and – besides direct image alignment – it uses the planes for tracking and global graph optimization. This way, our method makes use of the dense image information available in keyframes for accurate short-term tracking. At the same time it uses a global model to reduce drift. Both components are integrated consistently in an expectation-maximization framework. In experiments, we demonstrate the benefits our approach and its state-of-the-art accuracy on challenging benchmarks.