The disappearance of Melanie Hall prompted a major missing persons inquiry.
Police have always said the case is still open
Police began their investigation after the 25-year-old disappeared from Cadillacs nightclub in Bath on 9 June 1996.
Despite a £10,000 reward offered for information, and a feature on a Crimestoppers special, no trace of the hospital clerical worker was ever found.
The last sighting was of Miss Hall sitting on a stool on the edge of the dance floor at Cadillacs nightclub at 0110 GMT.
We hope this is the breakthrough the police need
Witnesses at the time said she had argued with her surgeon boyfriend with whom she had gone to the club.
Police confirmed that neither of the men arrested on Wednesday was Miss Hall's
Officers have always said the case is still open, and carried out extensive searches of the River Avon several times since 1996.
In 1998 a news conference was convened, and a fresh appeal for information launched by Miss Hall's family.
Detectives have also looked at possible links with other cases, including that of estate agent Suzy Lamplugh and the "Batman rapist", a
serial sex attacker in Bath who has evaded capture for years.
Miss Hall's parents are in their 50s and live in Bradford-on-Avon, eight miles from Bath.
In a short statement to the media, they said on Wednesday: "It is far too early to know whether this will finally lead to the truth about what happened to our daughter.
"We hope this is the breakthrough the police need."
Two men were arrested in connection with Miss Hall's disappearance on Wednesday.