Full Idea
One of the most popular semantic theories of truth is Kripke's theory. It describes a class of models which themselves involve a truth predicate (unlike Tarski's semantic theory).
Gist of Idea
Kripke offers a semantic theory of truth (involving models)
Source
report of Saul A. Kripke (Outline of a Theory of Truth [1975]) by Leon Horsten - The Tarskian Turn 02.3
Book Reference
Horsten,Leon: 'The Tarskian Turn' [MIT 2011], p.20
A Reaction
The modern versions explored by Horsten are syntactic versions of this, derived from Feferman's axiomatisation of the Kripke theory.