We propose an online 3D semantic segmentation method that incrementally reconstructs a 3D semantic map from a stream of RGB-D frames. Unlike offline methods, ours is directly applicable to scenarios with real-time constraints, such as robotics or mixed reality. To overcome the inherent challenges of online methods, we make two main contributions. First, to effectively extract information from the input RGB-D video stream, we jointly estimate geometry and semantic labels per frame in 3D. A key focus of our approach is to reason about semantic entities both in the 2D input and the local 3D domain to leverage differences in spatial context and network architectures. Our method predicts 2D features using an off-the-shelf segmentation network. The extracted 2D features are refined by a lightweight 3D network to enable reasoning about the local 3D structure. Second, to efficiently deal with an infinite stream of input RGB-D frames, a subsequent network serves as a temporal expert predicting the incremental scene updates by leveraging 2D, 3D, and past information in a learned manner. These updates are then integrated into a global scene representation. Using these main contributions, our method can enable scenarios with real-time constraints and can scale to arbitrary scene sizes by processing and updating the scene only in a local region defined by the new measurement. Our experiments demonstrate improved results compared to existing online methods that purely operate in local regions and show that complementary sources of information can boost the performance. We provide a thorough ablation study on the benefits of different architectural as well as algorithmic design decisions. Our method yields competitive results on the popular ScanNet benchmark and SceneNN dataset.