The name of the hall honors three generations of the Alexander family, who all served as University trustees.

Construction on the building was completed in 1894, and Alexander Hall held its first annual Commencement ceremony on June 13 of that year.

Following its renovation in the 1980s, the hall now has an elevator-mounted orchestra pit, sound reflectors for improved acoustics, humidity-controlled instrument storage, and a Tiffany Glass mosaic named "Homeric Story".

[3] Today, the building's turrets, rusticated brownstone, and red granite-walls frequently host concerts featuring ensembles and musicians, including conductor Gustavo Dudamel[6] in 2018 and 2019.

[7] Beyond music, the hall maintains a strong bond with the local community as a regular venue for town meetings, and it still occasionally serves as a venue for large student events, famous guest speakers, as well as for other various University affairs.