The genus Delphinus was first proposed by French naturalist Pierre Joseph Bonnaterre in 1789 to designate the common dolphin, then known as the _Dauphin commun_ (common dolphin) and the _Dauphin vulgaire_ (vulgar dolphin). The name is derived from Latin and means "dolphin" or "sea creature with a curved back."

Over time, multiple different dolphin species have been classified under the genus Delphinus, but many of them have since been moved to different genera. Some of the most notable historical species descriptions for Delphinus include:

- Delphinus capensis proposed by Gray (1828), now known as _Stenella capensis_ (_clymene dolphin_)

- Delphinus delphis originally named by Linnaeus in 1758, now recognized as _Delphinus delphis_ (common dolphin)

- Delphinus truncatus proposed by Montague in 1821, now recognized as _Tursiops truncatus_ (bottlenose dolphin)

As scientific understanding of dolphin taxonomy progressed, many additional species were described, and the original Delphinus genus was split into several distinct genera, including:

- Delphinus (the genus was restricted to the common dolphin)

- Lagenodelphis (formed for _Delphinus hosei_)

- Sousa (formed for _Delphinus chinensis_)

- Stenella (formed for _Delphinus frontalis_)

- Tursiops (formed for _Delphinus truncatus_)

The history of Delphinus has been marked by various revisions, taxonomic classifications, and the recognition of genetic and morphological differences among dolphin species. Consequently, the genus Delphinus has been refined over time, ultimately being reserved for the common dolphin, with multiple other historical "Delphinus" species now assigned to their own respective genera.