Plasmids are universally present in bacteria and play key roles in the dissemination of genes such as antibiotic resistance determinants. Major concepts in Plasmid Biology derive from the efforts to classify plasmids. Here, we review the main plasmid classification systems, starting by phenotype-based methods, such as fertility inhibition and incompatibility, followed by schemes based on a single gene (replicon type and MOB class), and finishing with recently developed approaches that use genetic distances between whole plasmid sequences. A comparison of the latter highlights significant differences between them. We further discuss the need for an operational definition of plasmid species that reveals their biological features, akin to plasmid taxonomic units (PTUs).