Plana was born in Havana. His family moved to Miami in 1960. He is a graduate of Loyola Marymount University and was trained in acting at the Royal Academy of Dramatic Art in London, United Kingdom. He has been married to actress Ada Maris since 1988 and they have two children.
While he is known to a broad audience for his roles in feature films and television, Plana is also known for his skills in acting and directing for the stage. He has created and directed a number of productions of the works of Shakespeare for minority audiences and he has been active in both the Los Angeles and New York City theater communities, including leading appearances on Broadway and at New York City's Public Theater. He originated the role of Rudy in the L.A. production of the Luis Valdez play Zoot Suit, going on to play Rudy in the film version as well.
Plana has acted, directed and written for television in series, mini-series, and specials such as Hill Street Blues, Star Trek: Deep Space Nine, Resurrection Blvd., Commander in Chief, CSI: Crime Scene Investigation, The West Wing, 24, Cagney & Lacey, and many others.
Plana has acted in films such as An Officer and a Gentleman, Three Amigos, Goal!, Lone Star, and others. He is known to PC gamers as the voice of Manny Calavera in the Lucasarts adventure game Grim Fandango.
From 2006 to 2010, Plana was a series regular on the ABC television series Ugly Betty, playing his most notable role, Ignacio Suares. In 2011, he joined the recurring cast of Desperate Housewives as Gabrielle's evil stepfather, Alejandro Perez, whose death became the driving force behind the main storyline of the series' final season.
Plana teaches acting at California State University, Dominguez Hills and Rio Hondo College.