The needs for accurate and efficient numerical solvers in computational aeroacoustics have motivated the development of low-dispersion and low-dissipation schemes as an alternative to more classical methods of applied mathematics for computational fluid mechanics over the last two decades. These numerical methods have now reached maturity, even if progress is still necessary to take account of specific physics. The paper provides a short overview of some recent developments and applications involving the direct computation of aerodynamic noise with applications to subsonic and supersonic jet noise, to cavity noise and to self-excited internal flows.