Seymour and, independently, Kelmans conjectured in the 1970s that every 5-connected nonplanar graph contains a subdivision of K_5. This conjecture was proved by Ma and Yu for graphs containing K_4^-. Recently, we proved the Kelmans-Seymour conjecture for all graphs. In this talk, I will give a sketch of our proof, and discuss related problems. This is joint work with Dawei He and Xingxing Yu.