Nuclear double beta decay provides an extraordinarily broad potential to search for beyond Standard Model physics, probing already now the TeV scale, on which new physics should manifest itself. These possibilities are reviewed here. First, the results of present generation experiments are presented. The most sensitive one of them -- the Heidelberg-Moscow experiment in the Gran Sasso -- probes the electron mass now in the sub eV region and will reach a limit of $\sim$ 0.1 eV in a few years. Basing to a large extent on the theoretical work of the Heidelberg Double Beta Group in the last two years, results are obtained also for SUSY models (R-parity breaking, sneutrino mass), leptoquarks (leptoquark-Higgs coupling), compositeness, right-handed W boson mass and others. These results are comfortably competitive to corresponding results from high-energy accelerators like TEVATRON, HERA, etc. Second, future perspectives of $\beta\beta$ research are discussed. A new Heidelberg experimental proposal (GENIUS) is presented which would allow to increase the sensitivity for Majorana neutrino masses from the present level of at best 0.1 eV down to 0.01 or even 0.001 eV. Its physical potential would be a breakthrough into the multi-TeV range for many beyond standard models. Its sensitivity for neutrino oscillation parameters would be larger than of all present terrestrial neutrino oscillation experiments and of those planned for the future. It could probe directly the atmospheric neutrino problem and even the large angle solution of the solar neutrino problem. It would further, already in a first step, cover almost the full MSSM parameter space for prediction of neutralinos as cold dark matter, making the experiment competitive to LHC in the search for supersymmetry.