Semantic tableaux for combined logical systems are usually constructed ad hoc and the problem of developing and applying more general methodologies for combining tableaux is yet to be systematically explored. In this talk I will address that problem and will outline some methodological approaches for combining tableaux for fibring, fusion, and products of logics. I will focus mainly on the case of fibring of tableaux and will discuss the questions of transfer of soundness, completeness, and termination from the components to the combined tableaux, both in general and in the context of some important special cases.