Much of our information about quasars is derived from their emission-line spectra. The analysis of such spectra has become an intricate subject which differs considerably from traditional, low-density nebular astrophysics. This review is intended to explain our present understanding of the situation, including some aspects of galactic nuclei whose luminosities are more modest than quasars. Quasars' line-emitting regions are probably photoionized (even if supplementary heating processes also occur). So far, models have been constructed which include ionization and thermal equilibria, the transfer of resonance-line and related photons, and the likely effects of absorption and scattering by dust grains. From comparisons between emission-line intensities produced in these models and observed quasars' spectra, it appears that certain densities and pressures and size scales occur in or around quasars. The relative abundances of elements are not very far from solar values, although it is suspected that heavy elements carbon, nitrogen, and oxygen in particular are moderately "overabundant" in quasars. The emission-line intensities also provide indirect information about quasars' ultraviolet and soft-x-ray continua; there are hints that photons with energies between 20 and 300 eV which are not directly observable may even represent the peak of the luminous output of a typical quasar. Finally, some gas-dynamical questions, while extremely important, are very difficult to answer, because of a lack of observables.