Conical carbon nanoparticles are a particular form of open carbon nanomaterials. Their typical structure follows from the presence of pentagonal disclinations within a seamless graphene sheet. As a result, two main carbon nanostructures are obtained: carbon nanocones and carbon nanohorns. They were discovered after fullerenes and carbon nanotubes and since then, they have been extensively studied, although their analytical applications are still to be exploited. This contribution compiles the main aspects of conical carbon nanoparticles, including their synthesis and properties as well as the functionalization procedures, which are different from those proposed for other carbon nanoparticles. Finally, the most relevant applications developed up to date are commented on.