The search for manifestations of physics beyond the Standard Model is one of the main directions of research at the LHC and future colliders under discussion. The effects caused by new physics can consist in the direct detection of new particles if their masses are less than the characteristic energies available at colliders and their interactions with SM particles are strong enough. But, if the masses of new particles are too large, or the interactions with SM particles are too weak, then new particles cannot be detected directly. In this case, the new physics can lead to a modification of the interactions of SM particles, to subthreshold effects. The review presents the current status of an approach or formalism called Standard Model Effective Field Theory (SMEFT), which allows one to describe and model deviations from the SM predictions in a theoretically consistent manner. The advantages and serious problems of this approach are discussed.