In the study of surface geometry, the uniformization theorem and the Gauss-Bonnet formula are of central importance. The former provides standard geometric models while the latter connects geometric and topological properties of a surface. In this talk, I will discuss higher-dimensional generalizations of these two results in a conformal-geometry context. In particular, I will talk about the Yamabe problem, the four-dimensional Gauss-Bonnet-Chern formula, and Q-curvature as important examples.