polynomial optimization is an important class of non-convex optimization problems, and has a powerful modelling ability for both continuous and discrete optimization. over the past two decades, the moment-sos hierarchy has been well developed for globally solving polynomial optimization problems. however, the rapidly growing size of sdp relaxations arising from the moment-sos hierarchy makes it computationally intractable for large-scale problems. in this talk, i will show that there are plenty of algebraic structures to be exploited to remarkably improve the scalability of the moment-sos hierarchy, which leads to the new active research area of structured polynomial optimization.