Polarized electron beams have played an important role in scattering experiments at moderate to high beam energies. Historically, these experiments have been primarily targeted at studying hadronic structure -from the quark contribution to the spin structure of protons and neutrons, to nucleon elastic form factors, as well as contributions to these elastic form factors from (strange) sea quarks. Other experiments have aimed to place constraints on new physics beyond the Standard Model. For most experiments, knowledge of the magnitude of the electron beam polarization has not been a limiting systematic uncertainty, with only moderately precise beam polarimetry requirements. However, a new generation of experiments will require extremely precise measurements of the beam polarization, significantly better than 1%. This paper will review standard electron beam polarimetry techniques and possible future technologies, with an emphasis on the ever-improving precision that is being driven by the requirements of electron scattering experiments.