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This thesis is dedicated to random walks on spaces with non-positivecurvature. In particular, we study the case of group actions on CAT(0) spacesthat admit contracting elements, that is, whose properties mimic those ofloxodromic isometries in Gromov-hyperbolic spaces. In this context, we proveseveral limit laws, among which the almost sure convergence to the boundarywithout moment assumption, positivity of the drift and a central limit theorem.In a second part, we study boundary maps and stationary measures on affinebuildings of type $\tilde{A}_2$, and we show that there always exists ahyperbolic isometry for a non-elementary action by isometries on such a space.Our approach involves the use of hyperbolic models for CAT(0) spaces, whichwere constructed by H.~Petyt, D.~Spriano and A.~Zalloum, and measured boundarytheory, whose principles come from H.~Furstenberg.

Marches al\'eatoires et \'el\'ements contractants sur des espaces CAT(0)