The standard model of the electroweak and strong interaction does not allow neutrinoless double beta decay but it is allowed in most Grand Unified Theories (GUT's). The neutrino must be a Majorana particle (identical with its antiparticle) and must have such a mass as to allow the neutrinoless double beta decay. Apart from one claim that the neutrinoless double beta decay in 76 Ge has been measured, one has only upper limits for this transition probability. But even the upper limits allow one to give upper limits for the electron Majorana neutrino mass and upper limits for parameters of GUT's and the minimal R-parity violating supersymmetric model. One can further give lower limits for the vector boson mediating mainly the righthanded weak interaction and the heavy mainly right-handed Majorana neutrino in left-right symmetric GUT's. For that one has to assume that the specific mechanism is the leading one for the neutrinoless double beta decay and one has to be able to calculate reliably the corresponding nuclear matrix elements. In the present contribution, we discuss the accuracy of the present status of calculating the nuclear matrix elements and the corresponding limits of GUT's and supersymmetric parameters.