  Modern redshift surveys such as the 2 degree field Galaxy Redshift Survey
(2dFGRS) and the Sloan Digital Sky Survey (SDSS) reveal the fully 3 dimensional
distribution of a million or so galaxies over a large cosmological volume.
Visually galaxies appear to be distributed along sheet-like and/or filamentary
superclusters. The CfA Great Wall, Southern Great Wall and the recently
discovered SDSS Great Wall are very spectacular superclusters. Clearly
theoretical predictions for galaxy clustering must be tested against these rich
datasets. This can be achieved by means of the Minkowski Functionals (MFs). A
MF-based approach provides an excellent description of superclusters and voids
and allows one to quantify the properties of the cosmic web. In this review we
give a summary of the progress made in this direction. After reviewing the
status of observations and of numerical simulations, we comment upon the nature
of bias which serves as a link between theoretical predictions and
observations. We also summarise the methods developed for efficient numerical
estimation of MFs for cosmological datasets and list several important results
obtained using these methods. Specifically, we stress the discriminatory power
of MFs and of the derived morphological statistics, the Shapefinders.
Shapefinders are an excellent tool with which to study the shapes and sizes of
superclusters and voids. We also discuss some of the important effects of
scale-dependent bias which are brought out by a MF-based study of the mock
catalogues of galaxies. Such effects, we note, should be accounted for before
comparing theoretical models with observations.
