(written from a Production point of view)
Joseph "Joe" D'Agosta (born 10 August 1935; age 85) was the casting director of Star Trek: The Original Series during its entire three-season run, starting with the first pilot, "The Cage". He was also the casting director of Mission: Impossible, The Lucy Show and Mannix at the same time, which were all produced by Desilu. D'Agosta started out as an actor, but very soon turned to casting.
D'Agosta worked as assistant casting director on Gene Roddenberry's series, The Lieutenant, which starred Gary Lockwood. However, after the controversial episode To Set It Right (guest starring Nichelle Nichols and Don Marshall), the US Navy withdrew its support from the series, and Roddenberry needed to hire extras from elsewhere. D'Agosta found a quick and cheap solution for this, and was thus promoted to the show's main casting director.
After The Lieutenant was cancelled, D'Agosta was hired by Twentieth Century Fox for a motion picture, but he turned down that offer, when Roddenberry contacted him to do the casting for his new science fiction project, Star Trek, feeling he would benefit much better from constant employment on a series than a few weeks' paycheck at Fox. (These Are the Voyages: TOS Season One, p. 46)
During his career in casting, spanning more than four decades, D'Agosta worked on both television and film. His credits include The Brady Bunch, and films such as Poltergeist II: The Other Side (1986). D'Agosta was married to actress Barbara Baldavin, whom he cast as Angela Martine in "Balance of Terror", "Shore Leave", and "Space Seed", and as Lisa in "Turnabout Intruder". Sean Morgan, a regular bit player on Star Trek was a college friend of D'Agosta, which lead to him being cast in smaller roles on the series. He was also a classmate of Ralph Maurer at acting school, and cast him in two episodes of Star Trek.