  I review the standard paradigm for understanding the formation and evolution
of cosmic structure, based on the gravitational instability of dark matter, but
many variations on this basic theme are viable. Despite the great progress that
has undoubtedly been made, steps are difficult because of uncertainties in the
cosmological parameters, in the modelling of relevant physical processes
involved in galaxy formation, and perhaps most fundamentally in the
relationship between galaxies and the underlying distribution of matter. For
the foreseeable future, therefore, this field will be led by observational
developments allowing model parameters to be tuned and, hopefully, particular
scenarios falsified. In these lectures I focus on two ingredients in this class
of models: (i) the role of galaxy bias in interpreting clustering data; and
(ii) the statistical properties of the initial fluctuations. In the later case,
I discuss some ideas as to how the standard assumption - that the primordial
density fluctuations constitute a Gaussian random field - can be tested using
measurements galaxy clustering and the cosmic microwave background.
