FUNCTION SPACES have played a crucial role in the genesis
of functional analysis from its very beginning, but equally for the
development of the modern analysis of partial differential (and pseudo-)
differential operators, distribution theory, interpolation theory,
or approximation theory.

During the last 50 years, partially through the heroic work of Hans
Triebel, whose 80th birthday is the reason for this meeting, the theory
has almost developed into an independent branch of analysis,
with a lot of expertise and knowledge being accumulated,
published in journals, at conferences and in particular in books.

It is the purpose of this talk to recapitulate a little bit some of the
concepts which have lead to the rich zoo of function spaces which we find
currently in the literature, but also shed some light on the problem:
``find the right space for a operator''!