  The Nonlinear Schroedinger Equation (NLSE) with a random potential is
motivated by experiments in optics and in atom optics and is a paradigm for the
competition between the randomness and nonlinearity. The analysis of the NLSE
with a random (Anderson like) potential has been done at various levels of
control: numerical, analytical and rigorous. Yet, this model equation presents
us with a highly inconclusive and often contradictory picture. We will describe
the main recent results obtained in this field and propose a list of specific
problems to focus on, that we hope will enable to resolve these outstanding
questions.
