Algebraic fibring, that is, combining logic systems by means of colimits in appropriate categories of logics, was introduced by A. Sernadas and his collaborators in 1999. The preservation by fibring of metaproperties of logics, such as soundness, completeness and interpolation, is one of the basic concerns in the subject of combining logics. In this talk we address the preservation by fibring of the different degrees of algebraization of logic systems stated in the so-called Leibniz Hierarchy (cf. Font, Jansana and Pigozzi, 2003). Thus, we prove that several categories of logic systems in the Leibniz hierarchy have constrained and unconstrained fibring: Protolagebraic logics, equivalential logics and (Blok & Pigozzi) algebraizable logics. Finally, the question of combining algebraizable logics from the semantical point of view is also analyzed. We prove that the category of matrix semantics and the category of equivalent algebraic semantics have constrained and unconstrained fibring. This is a joint work with Victor Fernández (National University of San Juan, Argentina).