The discovery of neutrino masses suggests that the Standard Model should be supplemented with new gauge-singlet fermions, often called sterile neutrinos. The interplay among the new couplings introduced in the Standard Model can accommodate the neutrino oscillation data for a variety of choices: the new particles can be extremely heavy and practically unobservable, or they can be light, in which case they can solve several long-standing puzzles. It has been shown, for example, that sterile neutrinos in some range of masses can account for dark matter, their emission from a supernova can explain pulsar kicks, and their decays can play an important role in the formation of the first stars. Though indirect, these clues indicate that sterile neutrinos can be the minimal solution to a variety of unsolved problems. This emphasizes the importance of investigating further the consequences of these new degrees of freedom for cosmology and astrophysics.;In this dissertation, I explore the possible role of sterile neutrinos of different mass scales in some cosmological and astrophysical phenomena.;A minimal extension of the Higgs sector of the Standard Model, with a gauge-singlet boson coupled to sterile neutrinos, can provide a consistent framework for the theory of neutrino masses, and can produce a relic population of keV sterile neutrinos via decays of the singlet Higgs. The latter can account for the dark matter of the universe. The mechanism operates around the electroweak scale, and has interesting consequences for the electroweak phase transition.;Relic sterile neutrinos produced via decays at the electroweak scale constitute colder dark matter than those produced via other previously suggested mechanisms. The primordial thermal content of dark matter has important implications for the formation of cosmic structures, such as clusters and galaxies. The assessment of the relevant properties suggests that sterile neutrinos produced at the electroweak scale are a compelling dark-matter candidate which may alleviate some of the discrepancies that appear between the traditional cold dark matter scenario and the observed small-scale structure of the universe.;Heavier and unstable sterile neutrinos may play an important role in compact astrophysical objects. Weakly coupled sterile neutrinos of mass of about 200 MeV, produced in the core of a supernova, can facilitate the energy transport from the core to the shock front. This is critical for the successful propagation of the shock in supernovae, and the fate of the star. The mediation of sterile neutrinos, which may be the missing piece of physics in the explosion mechanism, yields an observable signature that can help test this scenario.
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