Traditionally, the term random numbers applies to pseudo-random numbers that arise from a uniform distribution whereas random variates applies to pseudo-random numbers generated from some other distribution. However, Gentle [49] points out that these two terms along with the additional term random deviates can all be used interchangeably. Regardless of the terminology that is ultimately used, high-quality random numbers are very important in a wide range of mathematical, statistical, engineering and scientific applications. For example, computer simulation of physical processes use random numbers to study system behavior under different scenarios in a virtual environment that mimics real-world conditions. Such studies often lead to significant improvements and optimization of system performance. Reliable sources of random numbers with statistical properties indistinguishable from true random numbers are therefore a fundamental necessity for successfully carrying out such tasks. In addition, computational resources for obtaining true random numbers from naturally occurring physical processes will also be provided later on in this chapter.