  Precision cosmology has recently triggered new attention on the topic of
approximate methods for the clustering of matter on large scales, whose
foundations date back to the period from late '60s to early '90s. Indeed,
although the prospect of reaching sub-percent accuracy in the measurement of
clustering poses a challenge even to full N-body simulations, an accurate
estimation of the covariance matrix of clustering statistics, not to mention
the sampling of parameter space, requires usage of a large number (hundreds in
the most favourable cases) of simulated (mock) galaxy catalogs. Combination of
few N-body simulations with a large number of realizations performed with
approximate methods gives the most promising approach to solve these problems
with a reasonable amount of resources. In this paper I review this topic,
starting from the foundations of the methods, then going through the pioneering
efforts of the '90s, and finally presenting the latest extensions and a few
codes that are now being used in present-generation surveys and thoroughly
tested to assess their performance in the context of future surveys.
