Geometrically accurate and semantically expressive map representations have proven invaluable to facilitate robust and safe mobile robot navigation and task planning. Nevertheless, real-time, open-vocabulary semantic understanding of large-scale unknown environments is still an open problem. In this paper we present FindAnything, an open-world mapping and exploration framework that incorporates vision-language information into dense volumetric submaps. Thanks to the use of vision-language features, FindAnything bridges the gap between pure geometric and open-vocabulary semantic information for a higher level of understanding while allowing to explore any environment without the help of any external source of ground-truth pose information. We represent the environment as a series of volumetric occupancy submaps, resulting in a robust and accurate map representation that deforms upon pose updates when the underlying SLAM system corrects its drift, allowing for a locally consistent representation between submaps. Pixel-wise vision-language features are aggregated from efficient SAM (eSAM)-generated segments, which are in turn integrated into object-centric volumetric submaps, providing a mapping from open-vocabulary queries to 3D geometry that is scalable also in terms of memory usage. The open-vocabulary map representation of FindAnything achieves state-of-the-art semantic accuracy in closed-set evaluations on the Replica dataset. This level of scene understanding allows a robot to explore environments based on objects or areas of interest selected via natural language queries. Our system is the first of its kind to be deployed on resource-constrained devices, such as MAVs, leveraging vision-language information for real-world robotic tasks.