Abstract
The effective interaction approach can describe the interaction between spin 0 and 1/2 dark matter and standard-model particles. The effective operator approach can be applied for those models in which the mass of the exchange force mediator are heavy. A light dark matter possess the magnetic or electric dipole moment can explain the event excess in the CoGeNT, DAMA, and CRESST, and mitigate the constraint from XENON100 due to the divergence of the dark matter-nucleus cross section at the low energy. The effects of these dark matter are studied. The dark matter-nucleus cross section for direct detection, the dark matter production cross section at the hardron colliders, the dark matter annihilation rate for indirect detection, and the dark matter capture and annihilation rate at Sun for solar neutrino experiments are considered in the contents. The interaction strengths of these dark matter have been constrained by the many sorts of dark matter experiments, and the limits for the interaction strengths are given in this work.