{\it Wiener amalgam spaces} (originally called {\it Wiener-type spaces}
have been introduced in full generality in the summer of 1980.
They allow to describe the {\it global behaviour} of some {\it local norm}. The most simple cases are spaces of the form $W(L^p,\ell^q)(R^d)$, with
$1 \leq p,q \leq \infty$, where the $\ell^q$-sum of the local
$L^p$-norms over the unit cubes sitting at $k \in Z^d$ is finite (and
defines the norm). In the more general case one has to make use
of somewhat smooth and uniform partitions of unity, such as the
basis functions (shifted B-splines) for the space of cubic splines.

{\it Product-convolution} or {convolution-product} operators are
concatenations of pointwise multiplication and convolution operators.
While pointwise multiplication may increase the decay of a given
function or distribution it is clear that a convolution operator
will typically improve the local properties (without changing the
global behaviour). Moreover, such operators are good regularizers
and thus appear in the theory of (ultra-)distributions, showing
how to approximate distributions by test functions.

We will discuss a few of such situations, and if time permits
we will also indicate some new results (joint work with Stevan Pilipovic
and Bojan Prangovski) concerning the characterization of some
new translation and modulation invariant Banach spaces of functions.