The studies of the abundances of superheavy chemical elements in magnetic stars conducted at the Crimean Astrophysical Observatory were facilitated by the launch of the Astron space station in 1983. This spacecraft observed the ultraviolet spectra of such stars. The present brief review is focused on the abundances of superheavy elements (Pt, Au, Hg, Tl, Pb, Bi, Th, and U) in the atmospheres of magnetic Ap and HgMn stars. These results were obtained basing on the visible and ultraviolet spectra of stars. The data accumulated over more than 30 years show that these stars are characterized by significant overabundances (up to 6–7 dex) of such elements. The following important fact is noted: the superheavy element anomalies follow the trend in the anomalies that are characteristic of less heavy elements. Therefore, it may be assumed that all these anomalies (including the significant overabundances of superheavy elements) share a common explanation. Certain unresolved problems are discussed briefly.