We present in this work well-resolved and accurate Direct Numerical Simulations (DNS) of droplet condensation. Despite the great scientific and industrial interest, to this day, there is not an extensive knowledge of the different processes involved in droplet condensation. Consequently, DNS should be considered as a promising tool to investigate on this phenomenon. A preliminary validation of our simulations is carried out by direct comparison with the quasi-static theory of the droplet condensation in an infinite vapour medium. Next, more complex configurations have been considered: the condensation of a moving droplet in a subcooled vapour flow and the condensation of a hemispherical droplet deposed on an isothermal flat surface. The latter represents a first step towards the understanding of the more demanding DropWise Condensation. In both configurations, the effects of the Jakob number,Ja, have been thoroughly analysed to understand how the condensation impacts on the droplet heat flux and dynamics. This has led to the definition of a particular condensation regime for the lower Ja values, hereinafter called low condensation rate regime, where the droplet heat transfer is independent of the Ja. By increasing theft!, instead, the effects due to condensation start to grow exponentially. This regime is referred as the high condensation rate regime in this paper. Finally, some general trends for correlations on the Nusselt number and drag coefficient accounting for condensation are proposed in this study. (C) 2018 Published by Elsevier Ltd.