Historically Wiener Amalgam spaces have allowed to define modulation spaces via uniform decompositions of tempered distributions on the Fourier transform side. Basic results concerning e.g. duality, pointwise multipliers or the equivalence of continuous and discrete norms (using partitions of unity) have been formulated in the even more general context of decomposition spaces.

The now traditional approach to modulation spaces, starting from their characterization by means of the short-time Fourier transform was a strong motivation for the development of coorbit theory, which provides a unified approach to wavelet theory, modulation spaces, but also many classical and new function spaces (e.g. related to the shearlet group).

As a special case of coorbit spaces, namely the ones obtained by making use of the Schroedinger representation of the reduced Heisenberg group, many results about general modulation spaces follow more or less directly by specialization of the general theory. However, this is sometimes not so obvious, and hence this talk is going to point out a few of these connections.