In this talk I will review the general ideas behind the recently developed relativistic effective field theories (EFTs) for different phases of matter (spontaneous symmetry breaking, Goldstone theorem, etc.). I will put particular emphasis on concretely building an EFT for the description of collective excitations in zero-temperature superfluids, which is the simplest of these theories. I will then argue that these methods, borrowed from high energy theory ideology, are mature enough to be successfully applied to phenomenologically relevant problems. In this direction, I will present two applications: (1) the calculation of the gravitational mass transported by a sound wave in a nonrelativistic medium (superfluid, fluid and solid), and (2) the study of the response of a He-4 detector to the passage of sub-MeV dark matter particle. ----- Follow the link in use since May 5th or contact the organisers (Antoine Bourget and Edoardo Vescovi). Student introduction at 13:00.