We give a brief review on anapole dark matter (ADM). In the ADM the dark matters interact with the ordinary matters exclusively through the electromagnetic anapoles. Meanwhile, the only allowed electromagnetic form factor for the spin 1/2 Majorana fermions is the anapole one. In this thesis, we study the electromagnetic interaction of the Majorana neutrinos in non-commutative standard model (NCSM) and the Lorentz violated extension of the standard model (SME). Consequently, we obtain the anapole form factors in the both models. We explore the dark matter annihilation cross-sections in NCSM to estimate a bound of the order of 0.5 TeV on the parameter of non-commutativity. Comparing the obtained results in the SME with the experimental data only put a bound on d 00 -parameter among the SME- parameters which is of the order of 0.2.