There are many controversies regarding the cyto- and genotoxicity of carbon nanotubes (CNTs). In this work, we discuss that many of the incongruous arguments are probably associated with the poor physical-chemical characterization of the CNT samples used in many publications. This manuscript presents examples of carbon nanostructures observed under high resolution electron microscopy that can be found in typical CNT samples, and shows which roles in cyto- and genotoxicity need to be better investigated. Issues concerning chemical treatment are addressed and examples of misunderstandings that can occur during the studies of cyto- and genotoxicity of CNT samples are given.