A large variety of Banach spaces of functions or distributions,
or spaces of analytic functions arising in complex analysis,
are connected with the action of certain groups.

Coorbit theory, as developed jointly with Karlheinz Groechenig
in the 80s allows to explore these spaces using
methods from group representation theory and mostly functional
analytic ideas, nowadays known is Banach frames or Riesz projection
bases. Such ideas are closely related to the question of sets of
interpolation and sets of sampling for suitable Hilbert or also
Banach spaces of (smooth) functions, including the transform
domain of e.g. the continuous wavelet transform or the
STFT (short-time Fourier transform).

In this introductory presentation a perspective to the topics
covered in the different presentations of this conference is
given, encouraging to transfer questions and results form one
setting to a related setting, where so far other questions may
be dominant.