Abstract: Topological superconductors, an emergent class of superconducting states, provide an ideal platform for the investigation of topology as well as parity symmetry. They also support the existence of Majorana anyons—quasiparticles that are their own antiparticles—with potential applications in fault-tolerant quantum computation. Scanning tunneling microscopy and spectroscopy are advanced experimental techniques widely used to study topological superconducting states due to their ultrahigh spatial and energy resolution. In this article, we briefly discuss the fundamental properties and theoretical models of topological superconductors and Majorana anyons, as well as recent experimental progress based on scanning tunneling microscopy. Overall, research on topological superconductors at the nanoscale is advancing rapidly, with numerous potential material platforms being realized and growing evidence for Majorana anyons being reported. However, multi-dimensional detection methods and more systematic experimental investigations are still needed to achieve a comprehensive understanding of the novel phenomena observed.