This chapter focuses on the set of theories that are based on equivalence. The chapter closes with a short presentation of relevance theory, which remains a theory of equivalence, and a consideration of equivalence as a functional social illusion: what people believe about equivalence may be more important than any actual testing of its existence. The main points covered in this chapter are: The solutions for directional equivalence tend to be expressed in terms of two opposed poles, where one pole stays close to start-text form and other modifies that form. For example, "formal correspondence" is opposed to "dynamic equivalence". Although there are usually more than two ways of translating, the reduction to two is part of way translation has been seen in Western tradition. The two polarities ensue from an assumed cultural and linguistic border. Directional equivalence solves the apparent "impossibility of translation" posited by structuralist linguistics. Equivalence becomes so possible that there are many ways of achieving it.