In the theory of reductive groups over local fields, Bruhat-Tits buildings are the analogues of symmetric spaces in the theory of Lie groups.
By Goldman-Iwahori, the Bruhat-Tits building of the general
linear group GL_n over a local field k can be described as the set of non-archimedean norms on the vector space k^n.
I will explain how via a Tannakian formalism this can be generalized to a concrete description of the Bruhat-Tits building of an arbitrary reductive group.
This also gives a description of the functor of points of Bruhat-Tits group schemes.