In a letter to Andre\' Weil in 1967, Langlands suggested the existence of a relation between two seemingly unrelated mathematical objects: Galois representations and automorphic representations. \vskip .1in \noindent Since then, the work of many mathematicians has focused on isolating and constructing algebraic varieties whose geometry is supposed to explain the existence of such correspondences. \vskip .1in \noindent For correspondences defined over a number field, this role is played by Shimura varieties. \vskip .1in \noindent In my talk I will discuss some aspects of the geometry of the Shimura varieties and how they reflect Langlands\' conjectures.