As of 2011, the record for its longest running show is held by the musical Hairspray, which opened August 15, 2002, and ran for 2,642 performances before closing on January 4, 2009.
Designed by architect Herbert J. Krapp, the developer, real estate mogul Alexander Pincus originally named it the "Alvin Theatre" as an amalgam of the names of producers ALex Aarons and Vinton Freedley. It opened on November 22, 1927, with George and Ira Gershwin's Funny Face starring Fred and Adele Astaire. In 1930, Ethel Merman made her Broadway debut in Girl Crazy; in 1934, she appeared again in Cole Porter's Anything Goes and again in 1936 in Porter's Red, Hot and Blue. In 1935, the Gershwins' American folk opera Porgy and Bess had its world premiere at the venue. Due to the Great Depression, Aarons and Freedley lost control of their venue in 1932. For a period, CBS used it as a radio studio. In 1960, Lucille Ball appeared in her only Broadway show, the musical Wildcat. In 1965, Liza Minnelli made her Broadway debut in Flora the Red Menace. The original Broadway production of Annie opened in 1977 and ran for nearly six years, setting a record for the Alvin.
In 1977, the Nederlander Organization purchased the structure and renamed it in honor of American playwright Neil Simon on June 29, 1983, while his play Brighton Beach Memoirs. was playing. In 1985, its sequel Biloxi Blues also played at the theatre.
The New York City Landmarks Preservation Commission designated the building a New York City landmark in 1985. Historical records show that the original seating capacity was 1,362; in 2002, it expanded from 1,328 to a potential 1,467 after the May 27, 2002, closing of Elaine Stritch at Liberty. (To use the orchestra pit, 26 seats must be removed.) Robin Williams was to perform five shows of his comedy tour, Weapons Of Self-Destruction at this theatre in early April 2009, but he was forced to cancel the engagement due to his health. In lieu of Williams, the revival of Ragtime, opened November 15, 2009, after a successful run at the Kennedy Center in Washington, D.C. It closed January 10, 2010, due to low ticket sales after only 28 previews and 57 regular performances.
The new musical Catch Me if You Can began previews on March 11, 2011, and opened on April 10, 2011. On September 4, 2011, Catch Me If You Can closed after 32 previews and 170 regular performances.
In July 2015, the Nederlander Organization sold the structure's air rights to a consortium planning a highrise tower on Seventh Avenue between 41st and 42nd Streets. The sale will have no impact on the facility.
- 1927: Funny Face
- 1930: Girl Crazy
- 1932: Mourning Becomes Electra
- 1933: Mary of Scotland
- 1934: Anything Goes
- 1935: Porgy and Bess
- 1936: Red, Hot and Blue
- 1937: I'd Rather Be Right
- 1938: The Boys from Syracuse
- 1940: There Shall Be No Night
- 1941: Lady in the Dark
- 1943: Something for the Boys
- 1946: Joan of Lorraine
- 1947: Life with Father
- 1948: Mister Roberts
- 1951: A Tree Grows in Brooklyn
- 1952: Two's Company
- 1954: House of Flowers
- 1955: No Time for Sergeants
- 1957: Rumple
- 1958: Bells Are Ringing
- 1959: Once Upon a Mattress
- 1960: West Side Story; Wildcat
- 1961: Irma la Douce
- 1962: A Funny Thing Happened on the Way to the Forum
- 1965: Flora the Red Menace
- 1966: Dinner At Eight (Revival)
- 1967: Rosencrantz and Guildenstern Are Dead; Sherry!
- 1968: The Great White Hope
- 1970: Company
- 1975: Shenandoah
- 1977: Annie
- 1981: Merrily We Roll Along
- 1982: Do Black Patent Leather Shoes Really Reflect Up?
- 1983: Brighton Beach Memoirs
- 1985: Biloxi Blues
- 1990: Jackie Mason: Brand New
- 1992: Jake's Women
- 1993: Cyrano: The Musical
- 1996: The King and I (Revival)
- 1999: The Scarlet Pimpernel
- 2001: The Music Man
- 2002: Elaine Stritch at Liberty
- 2002: Hairspray (2,642 performances)
- 2009: Ragtime (Revival - 57 performances)
- 2010: Harry Connick Jr.: In Concert on Broadway
- 2010: RAIN – A Tribute to the Beatles
- 2011: Catch Me If You Can
- 2012: Jesus Christ Superstar (Revival)
- 2012: Scandalous
- 2013: Big Fish (34 previews and 98 performances)
- 2014: All the Way
- 2014: The Last Ship (29 previews and 105 performances)
- 2015: Gigi (20 previews, 86 performances)
- 2015: The Illusionists (62 performances)
- 2016: Cats (Revival)
- 2018: Angels in America (Revival)
- 2018: The Cher Show