Neutrinoless double beta decay is a lepton number violating process which is not allowed in the Standard Model (SM) of the electroweak interaction. The discovery of this process will be an unambiguous confirmation of the existence of New Physics outside the SM. At this moment many experiments are being conducted aimed at searching for neutrinoless double beta decay on various isotopes (76Ge, 136Xe, 130Te, 100Mo, etc.). The paper presents a brief overview of the results of some current projects, such as GERDA, MAJORANA, KamLAND-Zen, EXO-200, CUORE and SuperNEMO, and plans for creating a new generation experiments.