The Solar Updraft Power Plant technology addresses a very challenging idea of combining two kinds of renewable energy: wind and solar. The working principle is simple: a Solar Updraft Power Plant (SUPP) consists of a collector area to heat the air due to the wide-banded ultra-violet solar radiation, the high-rise solar tower to updraft the heated air to the atmosphere, and in between the power conversion unit, where a system of coupled turbines and generators transforms the stream of heated air into electric power. A good efficiency of the power plant can only be reached with extra-large dimensions of the tower and/or the collector area.The paper presents an up-to-date review of the SUPP technology, focusing on the multi-physics modeling of the power plant, on the structural behavior of the tower and, last but not least, on the modeling of the stochastic wind loading process.