The radiative corrections to the electron-electron scattering to order ${\mathrm{\ensuremath{\alpha}}}^{3}$ are calculated for (1) the colliding beam experiment and (2) the experiment in which the target electron is at rest initially. The contributions from high-energy real photons are included. The two-photon exchange diagrams are found to give only negligible contributions to the cross sections after infrared cancellation. The effect due to the possible breakdown of quantum electrodynamics is discussed. A preliminary study on the electron-positron colliding beam experiment involving various interactions is made. The vacuum polarizations involving heavier particles than an electron pair in the closed loop are investigated.