Discrete difference equations generalize differential equations. In a similar spirit, divided difference operators generalize partial differentiation operators. Though such operators go back to Newton, there has a been a resurgence of interest in them since the work of Lascoux and Schutzenberger on Schubert polynomials. While partial differentiation operators satisfy commutativity relations $\partial_x \partial_y = \partial_y \partial_x$, the divided difference operators satisfy the nilHecke relations. This gives the discrete operators a certain richness that is not present in the continuous operators.