A review of the role of multibody effects in the behavior of oligomer
bound states, crystalline structures, adsorption properties of surface
s and dense states of matter is given. Special emphasis is placed on t
he work of W. Kolos and coworkers in the Universities of Warsaw and Me
xico. New results including electron correlation are given here, confi
rming the enormous role played by the multibody corrections in the sta
bility of metallic clusters as Li-n and Be-n, where nonadditive effect
s are very large, to the point of making the convergence of the multib
ody expansion of the energy extremely doubtful. For polyatomic molecul
ar clusters as (NH3)(3) multibody effects albeit small, still are quit
e relevant to determine the cluster stability and geometry.