As Cohen-Macaulay modules on toric varieties behave very nicely in the way that they satisfy a version of Serre duality, they are of great interest. So the classification of these modules is a relevant problem. I will talk about one of the main results in this field of Bruns and Gubeladze who showed, that on toric varieties there are only finitely many maximal Cohen-Macaulay sheaves (up to isomorphism) of the form O_X(D), with D a Weil divisor.