Dentistry

Dentistry was the study and professional care of a person's teeth. A dentist was a person who practiced dentistry.

Most Starfleet medical personnel are trained in numerous fields, including dentistry. But there was also a dedicated sub-division of Starfleet Medical, Starfleet Dental, responsible for Dentistry. 

Dentists
In the 19th century on Earth, Doc Holliday was the local doctor and dentist of Tombstone, Arizona. 

In the 20th century, Maury Ginsberg was a very successful orthodontist in Scarsdale, New York. Orthodontics is the application of "braces" on a person's teeth, to realign teeth that would naturally fall out of alignment. 

In the latter-half of the 20th century, time-traveler Dr. Leonard McCoy was sarcastically accused of holding a degree in dentistry by a surgeon preparing to operate on fellow temporally-displaced patient Pavel Chekov at Mercy Hospital. 

Dental practices
Doctor Phlox had many degrees in alien medicine, among them was a degree in dentistry. 

On Vulcan, a common dental practice is for a Vulcan to have their teeth coated in a trifluorinate compound to prevent cavities. Despite having this done in 2128, T'Pol had a cavity in one of her tricuspids that Dr. Phlox had to restore in 2151. 

The inhabitants of planet 892-IV utilized a dental hygiene product known as Mars Toothpaste in 2268. 

In the Ferengi and Klingon cultures, teeth are sharpened with a tooth sharpener. 

Background
In the novel, Chain of Attack, a Dr. Rajanih was the doctor in charge of dentistry on board the USS Enterprise (NCC-1701).

Concept art for the USS Enterprise (NCC-1701-D) had a dental ward adjacent to sickbay.