The condensation of pure steam flowing downward inside a vertical tube has been extensively studied. Considerable amount of experimental and analytical efforts can be found due to the significance of this subject in practice. In this work, a critical review of the most important experimental, analytical and computational fluid dynamic (CFD) investigations have been presented. CFD simulations for the geometries of Goodykoontz and Dorsch [Goodykoontz and Dorsch, NASA TN D-3326, 1966; Goodykoontz and Dorsch, NASA TN D-3953, 1967], Kim and No [Kim and No, Int. J. Heat Mass Transf. 2000;43:4031–4042] and the present work have been performed and compared with the experimental data reported in these investigations. CFD predictions of the pressure drop and the heat transfer coefficient (HTC) were in close agreement with the experimental values. A preliminary regime map has been constructed for downward flow steam condensation inside pipes. Finally, all the published semi-empirical correlations for the HTC have been critically analysed and compared with the CFD predictions. An attempt has been made to make specific recommendations.