 The idea underlying the design of Frege and Russell’s logical deduction systems is that the theorems should be the formulas that correspond (intuitively) to the logical truths or logical validities. The concept of logical consequence was not central to the development, and this was also the case in the many systems of non-classical logics that were to be designed following in the footsteps of the first modal systems of C.I. Lewis. This situation influenced the way in which the research on some non-classical logics has usually been presented and sometimes also its real evolution. However, the concept of logical consequence has been the one that logic has traditionally dealt with. Tarski put it once again into the center of modern logic, both semantically and syntactically. Nowadays, a general theory of the algebraization of logics around the concept of logical consequence has grown from the different algebraic treatments of the different logics obtained during the last century.