Pseudo-random numbers are produced by recursive algorithms – i.e. the current number is calculated from one or a greater number of previous numbers. Thus, strictly speaking, the pseudo-random numbers are deterministic, not random. On the other hand, in many respects pseudo-random numbers behave like truly random numbers.
Pseudo-random numbers are widely used in Monte Carlo simulation and in related applications, e.g. in the relatively new and powerful branch of practical statistics known as resampling.
See also short courses
and the online book Resampling: The New Statistics.