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Non-positively curved spaces admitting a cocompact isometric action of anamenable group are investigated. A classification is established under theassumption that there is no global fixed point at infinity under the fullisometry group. The visual boundary is then a spherical building. When theambient space is geodesically complete, it must be a product of flats,symmetric spaces, biregular trees and Bruhat--Tits buildings.  We provide moreover a sufficient condition for a spherical building arisingas the visual boundary of a proper CAT(0) space to be Moufang, and deduce thatan irreducible locally finite Euclidean building of dimension at least 2 is aBruhat--Tits building if and only if its automorphism group acts cocompactlyand chamber-transitively at infinity.

An indiscrete Bieberbach theorem: from amenable CAT(0) groups to Tits buildings