We study the total sum of Grothendieck residues of a Laurent polynomial relative to a family f1,…,fn of sparse Laurent polynomials in n variables with a finite set of common zeroes in the torus T = (C*)n. Under appropriate assumptions we may embed T in a toric variety X in such a way that the total residue may be computed by a global object in X, the toric residue. This yields a description of some of its properties and new symbolic algorithms for its computation.