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This thesis focuses on the elaboration of numerical models of Fe II emission spectra and applications of these models to the interpretation of new observational data. A model of the Fe II atom, which includes the lowest 371 energy levels (up to 11.6 eV) and predicts intensities of 68635 lines, is first developed and then incorporated into the radiative-collisional code Cloudy. The atomic data and numerical methods used to determine level populations are described. The basic equations of ionization and thermal balance, level populations, and radiative transfer are solved self-consistently. Test cases show that the atom goes to local thermodynamical equilibrium in the limits of high particle and radiation densities.

The quantitative models have been applied to simulate emission spectra of H II regions. The general behavior of the Fe II emission lines and their sensitivity to density and radiative pumping conditions are investigated. New spectroscopic observations of the Orion Nebula obtained at the Cerro Tololo Inter-American Observatory are presented. The spectral range is 3498 -- 7468 A. The spectra are of high resolution and sensitivity and result in the most extensive line atlas of the Orion Nebula yet made. More than 400 emission lines have been identified, including 40 forbidden [Fe II] lines. Our theoretical model of Fe II emission is in good agreement with the observational data. The velocity field in the Orion Nebula, which shows a marked dependence on the ionization structure, has been analyzed. An overview is presented of general features of the Fe II spectra of typical quasar Broad Emission Line Regions and the dependence of these features on the basic parameters (density, flux of radiation, microturbulent velocity, the Fe abundance, and Ly-pumping). Calculations of Fe II emission for grids spanning several orders of magnitude in density and ionizing flux are performed in the framework of "locally optimally-emitting clouds." It is shown that strong selection effects are at work.

Due to the richness of the Fe II spectra and their sensitivity to the excitation parameters, the Fe II emission lines provide a powerful tool for diagnostics of physical conditions and Fe abundance in a variety of astronomical objects.