Experimental and theoretical work is reviewed on the two-dimensional system of electrons suspended above the surfaces of certain cryogenic dielectrics (liquid $^3$He and $^4$He and liquid and solid hydrogen) by the image force and an external electrostatic field. The stability of the system is studied. The electron properties determined by the interactions of the electrons with each other, with vapor atoms, and with thermal vibrations of the liquid surface are studied. A study of nonlinear effects is reported.