  The last few years have seen a surge in excitement about measurements of
statistics of the primordial fluctuations beyond the power spectrum. New ideas
for precision tests of Gaussianity and statistical isotropy in the data are
developing simultaneously with proposals for a wide range of new theoretical
possibilities. From both the observations and theory, it has become clear that
there is a huge discovery potential from upcoming measurements. In this Special
Issue of Advances in Astronomy we have collected articles that summarize the
theoretical predictions for departures from Gaussianity or statistical isotropy
from a variety of potential sources, together with the observational approaches
to test these properties using the CMB or large-scale structure. We hope this
collection provides an accessible entry point to these topics as they currently
stand, indicating what direction future developments may take and demonstrating
why these questions are so compelling. The Special Issue is available at
http://www.hindawi.com/journals/aa/2010/si.gsiu.html, and individual articles
are also available on the arXiv.
