Single-chain polymeric nanoparticles are artificial folded soft nano-objects of ultra-small size which have recently gained prominence in nanoscience and nanotechnology due to their exceptional and sometimes unique properties. This review focuses on the current state of the investigations of click chemistry techniques for highly-efficient single-chain nanoparticle construction. Additionally, recent progress achieved for the use of well-defined single-chain nanoparticles in some promising fields, such as nanomedicine and catalysis, is highlighted.