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--><!-- Kateryna Akbash and Ivan MatsakVolodymyr Vynnychenko Central Ukrainian State Pedagogical University,Kropyvnytsky, UkraineTaras Shevchenko National University of Kyiv, Ukraine Part of the Book: Stochastic Processes: Fundamentals and Emerging Applications Chapter DOI:https://doi.org/10.52305/ORAC1814 Abstract This chapter presents a review of studies of the almost sure asymptotic behavior of extremal values of independent identically distributed random variables and stochastic processes. The central result here is the law of the iterated logarithm for lim sup, the law of the triple logarithm for lim inf and some of its refinements. Among random processes, regenerative processes, birth and death processes, and processes in queuing systems are considered. 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