G. Boole and A. De Morgan created mathematical logic in the middle of the 19th century, by introducing mathematical models into logic. Boolean Algebras are the algebraic model of classical (two-valued) logic. They were introduced by G. Boole, in 1854, in his book “An Investigation of the Laws of Thought” (see [4]). This books has had a huge impact on the development of human society. Algebra of logic has developed in close connection with mathematical logic, being a distinct branch of Algebra with many applications. Residuated lattices, introduced by Krull in 1924, play the role of semantics for a multiple-valued logic called residuated logic. Residuated logic is a generalization of intuitionistic logic. Therefore, it is weaker than classical logic. Important examples of residuated lattices related to logic are Boolean algebras corresponding to basic logic, BL algebras corresponding to Hajek logic and MV algebras corresponding to Łukasiewicz many valued logic. The main scope of this chapter is to establish connections between the variety of Boolean algebras and other subvarieties of residuated lattices (with strong connections with Boolean algebras).