The Tate–Voloch conjecture says that given a closed subvariety $X$ of a semiabelian variety $G$ over $\mathbb{C}_p$, the distance between $X$ and any torsion point in $G\setminus X$ is uniformly bounded away from 0. This conjecture was proved by Scanlon in the case where $G$ is defined over $\overline{\mathbb{Q}_p}$. In this talk we discuss the history and subtleties around this conjecture, as well as how it may be used to prove results on integral torsion points in abelian varieties.