Buildings of spherical type are simplicial complexes which are closely related to semisimple algebraic groups. They were introduced and classified (for irreducible rank greater than 2) by Jacques Tits. One of the most important features in the theory of spherical buildings is the concept of opposition, which geometrically reflects the opposition relation between parabolic subgroups of semisimple groups. Opposite parabolics also play an important role in the more recent theory of Kac-Moody groups (of "minimal type"), which can be considered as inifinite-dimensional generalizations of semisimple groups. The corresponding geometric objects are twin buildings, which were introduced in the late 1980's by Ronan and Tits and generalize spherical buildings. In the talk, some group theoretic results (presentations; homological finiteness properties) will be discussed which heavily rely on the geometry/topology of the (twin) buildings these groups are acting on.