PtBi₂ is a polymorphic material that can crystallize in different (meta-)stable forms. Historically, it is best known for its pyrite (cubic) form, which displays an extremely large, nonsaturating magnetoresistance. In the last decade, a new crystal form of PtBi₂ has attracted considerable attention: trigonal PtBi₂. It crystallizes in the space group P31m and is a van der Waals layered material. Density functional theory predicts it to be a topological Weyl semimetal, with symmetry-protected topological band crossings lying near the Fermi energy. This particular electronic band structure leads to the formation of topological surface states known as Fermi arcs, which have been observed by spectroscopic techniques. In addition to its topological properties, trigonal PtBi₂ has been found to undergo a superconducting transition at low temperatures, as evidenced by transport experiments as well as with spectroscopic methods (angle-resolved photoelectron spectroscopy and scanning tunneling microscopy). Various strategies have also been explored to enhance the superconductivity in PtBi₂, including point contact, doping, and pressure-induced methods, which are also discussed in this review. This review begins with an overview of the synthesis, crystal symmetry, and electronic structure of trigonal PtBi₂. It then provides a comprehensive summary and analysis of recent advances in understanding its superconductivity and topological properties. Finally, the review discusses the potential applications of this material, for instance, in uncovering and engineering exotic quantum states, as well as its promises for realizing unconventional pairing mechanisms and topological superconducting phases.