  This review revolves around the question which general distribution of
scatterers (in a Euclidean space) results in a pure point diffraction spectrum.
Firstly, we treat mathematical diffration theory and state conditions under
which such a distribution has pure point diffraction. We explain how a cut and
project scheme naturally appears in this context and then turn our attention to
the special situation of model sets and lattice substitution systems. As an
example, we analyse the paperfolding sequence. In the last part, we summarize
some aspects of stochastic point sets, with focus both on structure and
diffraction.
