For over two decades, polymer brushes have found wide applications in industry and scientific research. Now, polymer brush research has been a significant research focus in the community of polymer science. In this review paper, we give an introduction to the synthesis, self-assembly, and applications of one-dimensional (1D) polymer brushes on polymer backbones, two-dimensional (2D) polymer brushes on flat surfaces, and three-dimensional (3D) polymer brushes on spherical particles. Examples of the synthesis of polymer brushes on different substrates are provided. Studies on the formation of the surface nanostructures on solid surfaces are also reviewed in this article. Multicomponent polymer brushes on solid surfaces are able to self-assemble into surface micelles (s-micelles). If the s-micelles are linked to the substrates through cleavable linkages, the s-micelles can be cleaved from the substrates, and the cleaved s-micelles are able to self-assemble into hierarchical structures. The formation of the surface nanostructures by coassembly of polymer brushes and "free" polymer chains (coassembly approach) or polymerization-induced surface self-assembly approach, is discussed. The applications of the polymer brushes in colloid and biomedical science are summarized. Finally, perspectives on the development of polymer brushes are offered in this article.