Greve Hall was completed in 1956 as a residence hall for women and was originally called West Hall. It was all double rooms, each of which had built-in dressers and closets. The architectural firm for the project was Barber and McMurry. It was named Greve Hall in 1963 and honored dean of women emeritus Harriet Greve, then 77 years old.
In the early years of the residence hall, two dances on the roof of the building were held. The fall dance was a mixer for new students, and the spring dance was for residents and their escorts. These two occasions were the only ones during which men students were allowed beyond the first floor lounge. To accommodate the festivities, building elevators were “expresses to the roof only” where a free jukebox and refreshments were provided.
In fall 1971 Greve was opened as an overflow hall for male students, providing temporary quarters until other housing could be found. The facility was closed in spring 1971 as a residence hall for economic reasons—there were empty beds enough in other halls to accommodate the residents of Greve. It was then used to house visiting athletes and high school students on weekends and was returned to service as a men’s residence hall for fall 1972. In August 1994 Greve became a coed dormitory, housing men on the first four floors and sorority women on the two top floors. Members of Sigma Kappa, Zeta Tau Alpha, and Delta Zeta sororities were housed on the top two floors. Housing for Sigma Kappa and Zeta Tau Alpha had been in Sophronia Strong Hall since 1992, but that housing did not provide the same level of opportunities as the housing in Massey for other sororities. Delta Zeta moved over to Greve from Massey. A third floor was devoted to sorority housing in fall 1995.
Greve Hall was removed from service as a residence hall in summer 2009, and a $9.4 million renovation repurposed it into an academic facility housing VolsTeach, the Bredesen CIRE program, and a variety of offices and special academic use facilities. The architectural firm for the conversion was the Lewis Group.