Mixing different components is the basis of chemistry. In heterogeneous catalysis, combinations of different active phases are frequently used, but involved in a mysterious way similar to alchemy. The language employed to describe such systems is typically imprecise due to the lack of clear definitions and efforts to quantify the observed performances. In this review, focused in the particular case of bifunctional catalysis, a set of definitions is provided aiming at an analytical and coherent examination of the literature. The works on hybrid zeolite based catalysts for hydroconversion processes are reviewed, and an attempt to classify the various origin of potential cooperation effects is provided. By such means, we hope to provide not only a clear view on the current state-of-the-art on hydroconversion catalysts but also a common framework for a more rigorous investigation of possible synergies of hybrid catalysts over all catalysed reactions.