General-purpose knowledge bases (KBs) are a cornerstone of knowledge-centric AI. Many of them are constructed pragmatically from web sources, and are thus far from complete. This poses challenges for the consumption as well as the curation of their content. While several surveys target the problem of completing incomplete KBs, the first problem is arguably to know whether and where the KB is incomplete in the first place, and to which degree. In this survey, we discuss how knowledge about completeness, recall, and negation in KBs can be expressed, extracted, and inferred. We cover (i) the logical foundations of knowledge representation and querying under partial closed-world semantics; (ii) the estimation of this information via statistical patterns; (iii) the extraction of information about recall from KBs and text; (iv) the identification of interesting negative statements; and (v) relaxed notions of relative recall. This survey is targeted at two types of audiences: (1) practitioners who are interested in tracking KB quality, focusing extraction efforts, and building quality-aware downstream applications; and (2) data management, knowledge base and semantic web researchers who wish to understand the state of the art of knowledge bases beyond the open-world assumption. Consequently, our survey presents both fundamental methodologies and the results that they have produced, and gives practice-oriented recommendations on how to choose between different approaches for a problem at hand. CCS Concepts: • General and reference → Surveys and overviews; • Computing methodologies → Knowledge representation and reasoning; Artificial intelligence.