We present SuperDec, an approach for creating compact 3D scene representations via decomposition into superquadric primitives. While most recent methods use geometric primitives to obtain photorealistic 3D reconstructions, we instead leverage them to obtain a compact yet expressive representation. To this end, we design a novel architecture that efficiently decomposes point clouds of arbitrary objects into a compact set of superquadrics. We train our model on ShapeNet and demonstrate its generalization capabilities on object instances from ScanNet++ as well as on full Replica scenes. Finally, we show that our compact superquadric-based representation supports a wide range of downstream applications, including robotic manipulation and controllable visual content generation. Project page: https://super-dec.github.io.