The technique of measuring the energy distribution of electrons which have been field emitted from a cold cathode is considered. The general historical and introductory theory is presented. A survey of the experimental techniques and existing energy analyzers is given. Specific studies on clean metal surfaces in which work functions, band structure effects, surface states, thermal effects, and many-body effects have been studied are reviewed from both the experimental and theoretical points of view. Field emission energy distributions have been particularly valuable in studies of atoms chemisorbed on surfaces. Several theories of enhanced resonance tunneling due to chemisorbed atoms are discussed. Specific systems studied experimentally are reviewed. Inelastic adsorbate enhanced tunneling is also treated.