The prediction of the maximum or minimum peaks of a random process in the fields of civil and mechanical engineering is a hot topic for the scientific literature. It is known that the maximum of a random process depends on the process length. For this reason, a probabilistic approach is necessary to estimate a reliable value from the process. Researchers for specific case of studies proposed several analytical models to predict maxima of a random process. Mostly, they are grouped on two families, models for Gaussian processes and models for non-Gaussian processes. Each model was computed and calibrated based on a specific experimental campaign for a specific case of study. This makes difficult to select the best model for every application. In addition, codes and standards neglect this topic and one might happen to make the error to assume the maximum value as the statistical maximum of the random process. Commonly, in the field of the structural engineering, peaks of a wind induced, or wind-induced flow acceleration time histories are estimated following the probabilistic approach of Cook and Mayne. However, from 1950 to today hundreds different probabilistic approach was given by literature. The purpose of this paper is to discuss an overview of models grouped by theoretical underlying assumptions.