Random number generation with multiple streams for sequential and parallel computing

We provide a review of the state of the art on the design and implementation of random number generators (RNGs) for simulation, on both sequential and parallel computing environments. We focus on the need for multiple independent streams and substreams of random numbers, explain how they can be constructed and managed, review software libraries that offer them, and illustrate their usefulness via examples. We also review the basic quality criteria for good random number generators and their theoretical and empirical testing.