This paper is written for specialists of surface techniques not perfectly familiar with catalysis, as well as for scientists working in the area of heterogeneous catalysis. It is aimed at suggesting the problems of characterization that surface analysis is faced with, because of the complexity of real catalysts. We first present the various typical 'architectures' to which catalysts may correspond. We shall then illustrate typical prohlems, and their solutions, by selecting examples in the field of hydrodesulfurization (HDS) catalysts. We shall show how 10 out of the 12 theories proposed for explaining catalytic activity were eliminated thanks to surface techniques. HDS catalysts are remarkable in several respects, especially because they undergo many 'metamorphoses' (activation, modifications during catalytic work, ageing, regeneration) from the time of their preparation to that of their death by irreversible deactivation. They therefore provide a large body of illustrative examples concerning the characterization of several 'architectures'. In spite of the achievements of surface techniques in clarifying many features of HDS catalysts during their life, investigators are still faced with unsolved problems; many such problems are related to the very fine scale (of the order of 1 nm or less) of the details of importance for catalysis. This might suggest directions for new improvements or the development of new surface techniques. As a conclusion, we shall recall that, because complete characterization needs the joint use of several techniques, a methodology of study had to be developed, now exists, and still continues to improve. The main lines of this general methodology are not restricted to catalysts, but can be used for the study of all complex highly dispersed solids.