  The present state of mathematical diffraction theory for systems with
continuous spectral components is reviewed and extended. We begin with a
discussion of various characteristic examples with singular or absolutely
continuous diffraction, and then continue with a more general exposition of a
systematic approach via stationary stochastic point processes. Here, the
intensity measure of the Palm measure takes the role of the autocorrelation
measure in the traditional approach. We furthermore introduce a `Palm-type'
measure for general complex-valued random measures that are stationary and
ergodic, and relate its intensity measure to the autocorrelation measure.
