We present a generalization of Macaulay’s Inverse System to higher dimensions. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. We extend Macaulay's correspondence characterizing the submodules of the divided powers ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras. We present effective methods for constructing Gorenstein graded rings with given numerical invariants fixed by their minimal free resolution. Recent generalizations by S. Masuti, M. Schulze and L. Tozzo will be presented. Possible applications are discussed.