This thesis describes methods that can be used to generate a sequence of pseudo-random numbers. Generators that are explained include middle square method, LCG, LFG, Mersenne Twister and ANSI X9.17 generator. The program implementation of the LCG and LGF generator is also shown. The results of the LCG program were tested with visual tests. Several sets of parameters were used, some of which were taken from established generators, and some of which were arbitrarily selected. One set of arbitrarily chosen parameters turned out to be bad, and the other gave satisfactory results. Some cryptographically secure generators (Blum Blum Shub, CryptMT and RSA generator) are also described. The problems of pseudo-random number generators in the context of cryptographic security are clarified. The thesis provides a historical overview of random numbers and their generators. It describes what makes a sequence of numbers random and what the differences are between truly random and pseudorandom numbers. For both groups of numbers, their limitations and advantages are explained. The same was done for true and pseudorandom number generators. Furthermore, various applications of pseudo-random number generators are presented and the thesis provides specific examples of these applications.