The Unit Graphs (UGs) framework is a graph-based knowledge representation (KR) formalism that is designed to allow for the representation, manipulation, query, and reasoning over linguistic knowledge of the Explanatory Combinatorial Dictionary of the Meaning-Text Theory (MTT). This paper introduces the UGs framework, and overviews current published outcomes. It first introduces rationale of this new formalism: neither semantic web formalisms nor Conceptual Graphs can represent linguistic predicates. It then overviews the foundational concepts of this framework: the UGs are defined over a UG-support that contains: i) a hierarchy of unit types which is strongly driven by the actantial structure of unit types, ii) a hierarchy of circumstantial symbols, and iii) a set of unit identifiers. On these foundational concepts and on the definition of UGs, this paper finally overviews current outcomes of the UGs framework: the definition of a deep-semantic representation level for the MTT, representation of lexicographic definitions of lexical units in the form of semantic graphs, and two formal semantics: one based on UGs closure and homomorphism, and one based on model semantics.