 The regular appeal to the notion of approximate truth by realists has several motivations. The widespread use of abstraction (that is, incorporating some but not all of the relevant parameters into scientific descriptions) and idealization (distorting the natures of certain parameters) suggests that even many of our best theories and models are not strictly correct. The common realist contention that theories can be viewed as gradually converging on the truth as scientific inquiry advances suggests that such progress is amenable to assessment or measurement in some way, if only in principle. And even for realists who are not convergentists as such, the importance of cashing out the metaphor of theories being close to the truth is pressing in the face of antirealist assertions to the effect that the metaphor is empty. The challenge to make good on the metaphor and explicate, in precise terms, what approximate truth could be, is one source of skepticism about realism. Two broad strategies have emerged in response to this challenge: attempts to quantify approximate truth by formally defining the concept and the related notion of relative approximate truth; and attempts to explicate the concept informally.