To autonomously navigate and plan interactions in real-world environments, robots require the ability to robustly perceive and map complex, unstructured surrounding scenes. Besides building an internal representation of the observed scene geometry, the key insight toward a truly functional understanding of the environment is the usage of higher-level entities during mapping, such as individual object instances. This work presents an approach to incrementally build volumetric objectcentric maps during online scanning with a localized RGB-D camera. First, a per-frame segmentation scheme combines an unsupervised geometric approach with instance-aware semantic predictions to detect both recognized scene elements as well as previously unseen objects. Next, a data association step tracks the predicted instances across the different frames. Finally, a map integration strategy fuses information about their 3D shape, location, and, if available, semantic class into a global volume. Evaluation on a publicly available dataset shows that the proposed approach for building instance-level semantic maps is competitive with state-of-the-art methods, while additionally able to discover objects of unseen categories. The system is further evaluated within a real-world robotic mapping setup, for which qualitative results highlight the online nature of the method. Code is available at https://github.com/ethz-asl/voxblox-plusplus.