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This is a survey about the connection between the representation theory of asemisimple group and the geometry of an affine building. The latter is,actually, associated to the Langlands'dual of the semisimple group. We deal,mainly, with the proof of the saturation theorem of Kapovich and Millson. Weobtain a simplification of their proof regarding the characterization of foldedtriangles. The article is written in french for it is the outcome of a seminarthat took place in Nancy last year.

Applications des immeubles en th\'eorie des repr\'esentations