A complete cycle of droplet nucleation, growth, coalescence and jumping on different textured hydrophobic and superhydrophobic surfaces is studied for the first time, using a 2-D double distribution function thermal lattice Boltzmann method. First, droplet nucleation mechanism on smooth and rough surfaces is studied in detail. The results reveal the presence of cooled vapor layer instability in the condensation on completely smooth surfaces. However, on the rough surfaces and near the roughness a completely different mechanism is observed and the nucleation occurs on the roughness wedges. Also, the condensation on different textured surfaces with nominal contact angles theta(a) = 90 degrees, 120 degrees, 155 degrees is studied. On all these surfaces it is observed that for small textures the nucleation occurs normally near the structure wedges. However, increasing the height of the textures displaces the nucleation sites to the top of the structure, near the structure edge. After growing the droplets different behaviors are observed for different contact angles, i.e., the Wenzel or suspended droplets are formed and the droplets even jump out. Moreover, based on the non-dimensional numbers a complete study of droplet jumping is carried out and a method for proper designing the textured surfaces is presented. Finally, the benefits of using hybrid textured surfaces and the mechanism of droplet jumping on these surfaces are explained. (C) 2019 Elsevier Ltd. All rights reserved.