The search for sterile neutrinos is an active area of particle physics for various reasons. First, new neutrino states have been advocated to understand unresolved puzzles in past data. Second, there are good theoretical justifications for introducing such heavy neutrinos. Finally, sterile neutrinos could explain the Dark Matter observed in our Universe. The aim of this book is to review the phenomenology of these hypothetical neutrino states and then to summarize the present existing constraints coming from both cosmology/astrophysics considerations and laboratory measurements.