The direct simulation of sound sources and sound fields in flows is a rapidly growing area in research of applied numerics. This particular branch of acoustics is known as Computational Aeroacoustics (CAA). the reason why CAA has been evolving so fast is twofold. Firstly, high accuracy solutions of the Euler's equations allow an adequate description of aeroacoustic source mechanisms. Secondly, CAA techniques are able to describe sound propagation through non-uniform flow fields. These two reasons distinguish CAA approaches to aeroacoustic problems from "classical" methods based on Helmholtz's wave equation, which is limited to low Mach number flows and requires the sources to be completely known in advance. At DLR, a CAA-code is under development, which will be used to predict airframe noise at high lift devices of aircraft. The source mechanism to be described numerically is the interaction of vorticity perturbations with geometric inhomogeneities and large scale hydrodynamic instabilities of the mean flow field. It includes acoustic and/or hydrodynamic feedback, i.e. resonance. High numerical accuracy in terms of spectral properties like dispersion error and dissipation is essential for the simulations. Therefore one challenge in CAA is to achieve highest accuracy also for complex flows and geometries, since these situations generally represent acoustic sources. In the past, CAA simulations have been mostly performed using spectrally tuned finite difference schemes on Cartesian grids. Some examples are given in the presentation. In future development one has to decide whether to use Cartesian grids throughout the domain and treat curved wall boundaries directly or to use locally body fitted grids in combination with background Cartesian grids. The problem of local grid size changes for neighbouring Cartesian grid blocks has to be addressed in view of efficiency and spectral accuracy. The presentation will point out some fundamental differences in the grid concepts between CFD and CAA. For example, the radiated acoustic wave structure generally is finer scale upstream than downstream. Furthermore, in contrast to CFD where the solution is usually sought in the immediate neighbourhood of the aerodynamic body, in CAA the solution in the far field is of primary interest.