Rate of penetration management is a matter of importance in drilling operations and it has been used in some research studies. Although conventional approaches for rate of penetration management are mainly focused on analytical and semi-analytical models, several correlations have also been developed for this purpose. The history of rate of penetration management studies extends back more than half a century and ever since, research interest in this concept has never declined, making it a focus of industry and academic studies. In this article, some of these studies are reviewed to achieve a better understanding of rate of penetration management concept, its financial benefits and also its research capacities. This review reveals the most common rate of penetration management methods which applied analytical, semi-analytical and empirical correlations in different fields around the world. In other words, the main purpose of this study is to evaluate the research studies in which different models and correlations have been used as the main approach for rate of penetration management. Based on the results of this review, the best models for performing rate of penetration management studies and the best objective functions for optimization algorithms are introduced.