  We discuss various analytical approximation methods for following the
evolution of cosmological density perturbations into the strong (i.e.
nonlinear) clustering regime. These methods can be classified into five types:
(i) simple extrapolations from linear theory, such as the high--peak model and
the lognormal model; (ii) {\em dynamical} approximations, including the
Zel'dovich approximation and its extensions; (iii) non--linear models based on
purely geometric considerations, of which the main example is the Voronoi
model; (iv) statistical solutions involving scaling arguments, such as the
hierarchical closure {\em ansatz} for BBGKY, fractal models and the
thermodynamic model of Saslaw; (v) numerical techniques based on particles
and/or hydrodynamics. We compare the results of full dynamical evolution using
particle codes and the various other approximation schemes. To put the models
we discuss into perspective, we give a brief review of the observed properties
of galaxy clustering and the statistical methods used to quantify it, such as
correlation functions, power spectra, topology and spanning trees.
