  Coorbit theory is a powerful machinery that constructs a family of Banach
spaces, the so-called coorbit spaces, from well-behaved unitary representations
of locally compact groups. A core feature of coorbit spaces is that they can be
discretized in a way that reflects the geometry of the underlying locally
compact group. Many established function spaces such as modulation spaces,
Besov spaces, Sobolev-Shubin spaces, and shearlet spaces are examples of
coorbit spaces. The goal of this survey is to give an overview of coorbit
theory with the aim of presenting the main ideas in an accessible manner.
Coorbit theory is generally seen as a complicated theory, filled with both
technicalities and conceptual difficulties. Faced with this obstacle, we feel
obliged to convince the reader of the theory's elegance. As such, this survey
is a showcase of coorbit theory and should be treated as a stepping stone to
more complete sources.
