General-purpose knowledge bases (KBs) are an important component of several data-driven applications. Pragmatically constructed from available web sources, these KBs are far from complete, which poses a set of challenges in curation as well as consumption. In this tutorial we discuss how completeness, recall and negation in DBs and KBs can be represented, extracted, and inferred. We proceed in 5 parts: (i) We introduce the logical foundations of knowledge representation and querying under partial closed-world semantics. (ii) We show how information about recall can be identified in KBs and in text, and (iii) how it can be estimated via statistical patterns. (iv) We show how interesting negative statements can be identified, and (v) how recall can be targeted in a comparative notion.