Structured commonsense knowledge about concepts and their properties is a foundational asset for building reliable AI applications. Previous projects like ConceptNet, TupleKB or Quasimodo have compiled substantial collections of such knowledge, yet have restrictions in terms of a simple datamodel, and limited precision and/or recall. In this paper we present a methodology and resource called ASCENT, advanced semantics for commmonsense knowledge extraction. ASCENT advances knowledge representation in CSKBs by enabling subgroups and aspects of concepts to be subjectss. Beyond existing quantitative rankings of KB assertions, ASCENT introduces also the notion of qualitative facets of assertions, allowing to capture, for instance, the location or time during which an assertion is true, or truth modifiers such as occasionally or frequently. Although these components are in principle known in knowledge representation and semantic role labelling, to our knowledge, this is the first time that such knowledge in this format is actually acquired at scale for commonsense. The extraction approach of ASCENT relies on a combination of automatically scoped web document retrieval and filtering, dependency-based open information extraction, and a consolidation stage relying on pretrained language models. Intrinsic and extrinsic evaluation point at the superior precision and recall of ASCENT. A web interface, data and code can be found at https://ascentkb.herokuapp.com.