Systematic first-principles calculations on transition metal (TM) impurities of the 3d series in Si have been performed. The equilibrium sites, migration energies, electrically-active gap levels, charge and spin states are predicted. While the properties of the isolated interstitials are experimentally well-known, much less experimental information is available about the consequences of their interactions with vacancy-like defects. We discuss here the properties of isolated interstitial Ti, Fe, and Ni, their interactions with vacancies and divacancies, the properties of the resulting substitutional impurities, and of the TM-divacancy {V-TM-V} complexes. In equilibrium, interstitial Ti, Fe, and Ni do not become substitutional, but a number of processing steps commonly used in PV manufacturing introduce highly mobile vacancies into the bulk. These vacancies strongly interact with interstitial TMs. At the substitutional site, Ti, Fe, and Ni have very different electrical properties than at the tetrahedral interstitial site. In particular, the electrical activity (and stable spin state) of Ti and Fe are greatly reduced, suggesting that the passivation by vacancies plays an unrecognized role during a variety of high-temperature processes.