Let $H$ be a given graph. A graph $G$ is $H$-linked if, for any injective map $\phi: V(H)\to V(G)$, $G$ contains a subdivision of $H$ rooted at the images of $V(H)$. A classic result of Seymour and Thomassen shows that every 4-connected plane triangulation is $K_2$-linked. Ellingham, Plummer and Yu proved that every 4-connected plane triangulation is $K_4^-$-linked. However, not all 4-connected surface triangulation is $K_4^-$-linked. In this talk, we focus on some recent developments on graph linkages on surfaces. This is based on joint work with Moser, Stephens, and Zha.