First-principles theory is used to calculate the interactions between interstitial iron or the iron-boron pair and a vacancy, between interstitial iron and a divacancy, oxygen-vacancy pair, self-interstitial, and interstitial carbon, as well as substitutional carbon, interstitial oxygen, and the oxygen dimer in silicon. The structures, charge and spin states, binding energies, and, in some cases, vibrational spectra are predicted. The gap levels are estimated using the marker method. The strongest interactions involve vacancies, result in the formation of pairs of metastable defects, and profoundly change the electrical activity of the component species. Iron also traps at self-interstitial-type defects, but not at interstitial oxygen or substitutional carbon. Several observed but incompletely characterized defects are identified and trends in the behavior of Fe in Si are discussed.