Increased computing power, resulting in ever-larger simulations, has placed additional demands on computer programs for generating random numbers. Periods that were once acceptable no longer are; defects have been found in the output of generators that were once considered acceptable; and methods for controlling pseudorandom streams on parallel processors still need improvement.

Techniques that simulate a Markov chain allow Monte Carlo methods to be used on increasingly complicated problems, especially analyses employing Bayesian approaches. Because these methods rely on a stationary distribution, questions of convergence of the process must be addressed.

This talk will review some of the recent developments both in the basic generators and in the simulation of iterative processes.