The nuclear matrix element (NME) | M 0 ν ν | cannot be measured independently; it must, but also can, be calculated. The calculation itself relies on sophisticated nuclear many-body theories and there exist different methods to do this. The NME | M 0 ν ν | differs also from nucleus to nucleus (i.e. chemical element to chemical element). Today, the calculation of the NME is a significant problem and it has been treated by different authors in different ways. One question is whether to treat the range of obtained values for | M 0 ν ν | as the theoretical uncertainty and whether this is then to be understood as a statistical uncertainty. Different approaches are being chosen here. The obtained values for | M 0 ν ν | often vary by factors of 2 up to about 5. Typical values lie in the range of from about 0.9 to 14, depending on the decaying nucleus/element.