We present DetectFusion, an RGB-D SLAM system that runs in real-time and can robustly handle semantically known and unknown objects that can move dynamically in the scene. Our system detects, segments and assigns semantic class labels to known objects in the scene, while tracking and reconstructing them even when they move independently in front of the monocular camera. In contrast to related work, we achieve real-time computational performance on semantic instance segmentation with a novel method combining 2D object detection and 3D geometric segmentation. In addition, we propose a method for detecting and segmenting the motion of semantically unknown objects, thus further improving the accuracy of camera tracking and map reconstruction. We show that our method performs on par or better than previous work in terms of localization and object reconstruction accuracy, while achieving about 20 FPS even if the objects are segmented in each frame.