Alonso was the first Latin American actress not born in the United States to star in a musical on Broadway, with Kiss of the Spider Woman at the Broadhurst Theatre (1995).

For what is considered her best known song, she was asked by Giorgio Moroder to write the lyrics in Spanish and sing "Vamos a Bailar" which he had written for the soundtrack of the film Scarface.

[6] Alonso sang the United States national anthem at the FIFA UNICEF charity match on July 27, 1986, at the Rose Bowl in Pasadena, California, in front of a crowd of 57,539.

[7][8] Alonso made her Hollywood film debut in Moscow on the Hudson (1984) with Robin Williams, and also starred in Touch and Go (1986), Extreme Prejudice (1987), The Running Man (1987), Colors (1988), Vampire's Kiss (1989), Predator 2 (1990) and The House of the Spirits (1993).

[10] Alonso was an outspoken critic of Cuba's Fidel Castro and Venezuelan President Hugo Chávez, whom she described as a "dictator"-like "Hitler"[11] and whose voters and supporters she described as "terrorists.

Alonso issued an "Open Letter to Sean Penn" (the two had played lovers in the 1988 movie Colors) online on March 29, 2010, regarding his support of Hugo Chávez.

[14] In 2008, Alonso endorsed the US presidential campaign of Republican nominee John McCain, writing:[15] As a Latina and a new American citizen, I believe in this country and its people, and I believe that we need more than just "change."

[16] In January 2014, Alonso resigned from a San Francisco production of The Vagina Monologues after appearing in an advertisement for Republican candidate for Governor Tim Donnelly.