Chapter 4 introduces the single-electron spectral function and the basic models for describing the measurement spectra of angle-resolved photoemission. It is shown that the photoemission density is proportional to the single-particle spectral function under the "sudden" approximation in the three-step model. This offers an irreplaceable tool for probing the momentum dependence of the energy gap as well as other single-particle properties of quasiparticle excitations. The Luttinger theorem, which relates the Fermi momentum with the filling factor of electrons, the particle-hole mixing, and the effect of quasiparticle scattering on the transport properties are also discussed.