We give an overview of the state of the art on the design and implementation of random number generators for simulation and general Monte Carlo sampling in parallel computing environments. We emphasize the need for multiple independent streams and substreams of random numbers, as well as the advantages (and potential pitfalls) of the increasingly popular counter-based and dynamically splittable generators. We look at recently-proposed constructions and software. We also recall the basic quality criteria for good random number generators and their theoretical and empirical testing. The paper outlines solutions and also raises issues that would require further study.