Since its publication in 1976, the Peng & Robinson equation of state (PR EoS) has become one of the most useful and successfully applied models for thermodynamic and volumetric calculations in both industrial and academic fields. For this reason, we have reviewed this cubic EoS, in order to explore the development around it and some general applications where it has been applied, including its most known modifications. So, a complete time-line of the PR EoS is presented, as a compilation of more than 200 modifications for pure compound applications and about 100 modifications for mixtures. These modifications to the PR EoS have been grouped in four main categories according to the nature of the modification: (a) by changing the dependence structure of a with temperature or the expressions for parameter a and b, (b) by introducing deviation functions (like volume translation), (c) by incorporating new parameters or terms in the equation of state, and finally (d) by modifying the mixing rules for mixture applications. Although great efforts have been made to improve accuracy and performance of the PR EoS, as demonstrated by the wide range of modifications, the necessity for further development of a universal, simple and accurate model is a rich source for research and discussion, considering the success of most of modifications is restricted to the studied properties and compounds, and therefore, they are limited to be just applied to the studied field. However, after 40 years, PR is still an invaluable and prominent tool, which will be under continuous development and research for next decades. (C) 2017 Elsevier B.V. All rights reserved.