The Poincaré duality theorem— that if M is an n-dimensional oriented, closed manifold, then the "dimension i” cohomology groups are isomorphic to the “codimension i” homology groups— has an analogue in the theory of group cohomology. This talk will give a brief introduction to group (co)homology before discussing the analogue of Poincaré duality for groups (known as Bieri-Eckmann duality). If there is time we will give an application to the cohomology of SL_n(Z), a current area of research.