  A proposal of how to complete non-relativistic quantum mechanics to a
physically meaningful, mathematically precise and logically coherent theory is
reviewed. Our proposal leads to a general, non-linear stochastic law for the
time-evolution of states of individual physical systems. An application of the
general formalism to the quantum theory of fluorescence of an atom coupled to
the radiation field is sketched. Some remarks on relativistic quantum theory
conclude our review.
