Mechanisms for three-body electron attachment to a molecule are examined. Methods for studying this process experimentally are described. The measurements of the characteristics of the process and their dependence on the parameters of the molecule and the energy of the electron are presented. It is shown that electron attachment to a molecule in a gas and a liquid are related. It is shown that three-body attachment is important in the low-temperature plasma of the upper atmosphere, high-pressure discharges, and gaseous dielectrics.