  Research done during the previous century established our Standard
Cosmological Model. There are many details still to be filled in, but few would
seriously doubt the basic premise. Past surveys have revealed that the
large-scale distribution of galaxies in the Universe is far from random: it is
highly structured over a vast range of scales.
  To describe cosmic structures, we need to build mathematically quantifiable
descriptions of structure. Identifying where scaling laws apply and the nature
of those scaling laws is an important part of understanding which physical
mechanisms have been responsible for the organization of clusters,
superclusters of galaxies and the voids between them. Finding where these
scaling laws are broken is equally important since this indicates the
transition to different underlying physics.
  In describing scaling laws we are helped by making analogies with fractals:
mathematical constructs that can possess a wide variety of scaling properties.
We must beware, however, of saying that the Universe is a fractal on some range
of scales: it merely exhibits a specific kind of fractal-like behavior on those
scales. We exploit the richness of fractal scaling behavior merely as an
important supplement to the usual battery of statistical descriptors.
  We review the history of how we have learned about the structure of the
Universe and present the data and methodologies that are relevant to the
question of discovering and understanding any scaling properties that structure
may have. The ultimate goal is to have a complete understanding of how that
structure emerged. We are getting close!
