Martinez was born Adolfo Larrue Martínez III in Glendale, California. His family referred to him as "A", "Little Adolfo" and "Little A" as a child to distinguish him from his father and grandfather. Over time, "A" became the name he would use. His heritage is Mexican. Martinez began his professional career at twelve years old as a singer earning him a talent competition title at the Hollywood Bowl. He graduated from Verdugo Hills High School in Tujunga, Los Angeles, CA. He was in a rock band in high school and was on the track team. He furthered his education and found his passion for acting at UCLA. He played on a semi-pro baseball team for five seasons.
Martinez has starred in feature films including The Cowboys (1972), Starbird & Sweet William (1973), Once Upon a Scoundrel (1974), Joe Panther (1976), Shoot the Sun Down (1978), The Honorary Consul (1983), Walking the Edge (1985), Powwow Highway (1989), She-Devil (1989), What's Cooking? (2000), and Wind River (2000).
The majority of his acting roles have been on television. He had a recurring role on All in the Family as a helper at Archie's bar. In 1974, he appeared in an episode of the short-lived ABC police drama Nakia. In 1978, he appeared as the Indian Circling Hawk in the short-lived ABC series The Young Pioneers. Mare Winningham was also cast on The Young Pioneers; she and Martinez married in 1981 but quickly divorced. Martinez appeared as Tranquilino Marquez in three episodes of the mini-series, Centennial in 1979.
In 1981, Martinez made an appearance on Barney Miller. He played Joseph Montoya in the episode "The Doll".
Martinez played a grape picker in 1982 on CBS's Falcon Crest, Native American Low Wolf on the short-lived Born to the Wind, and a police detective in the 1983–1984 series Whiz Kids. He was introduced to daytime viewers in Santa Barbara as Cruz Castillo, a role he played from the show's debut in 1984 until 1992; he won a Daytime Emmy in 1990. From 1999–2002, Martinez appeared on General Hospital playing mobster and FBI informant Roy DiLucca. During his time with General Hospital, he was awarded three consecutive ALMA Awards (2000, 2001, 2002). Since Martinez resembles Asher Brauner, who played the role 1978–1979, Martinez's flashbacks of his character did not need to be re-filmed. Martinez has also worked on prime time television, including starring roles in series such as Profiler and L.A. Law.
In September 2008, Martinez joined the cast of the ABC daytime drama One Life to Live in the role of Ray Montez and was written out in June 2009.
In February 2011, Martinez appeared in several episodes of the CBS daytime drama The Bold and the Beautiful as Dr. Ramon Montgomery. He returned in January 2012 for a few additional episodes.
In 2012, he landed the recurring role of Jacob Nighthorse in the television series Longmire.
In April 2014, it was rumored he was joining The Young and the Restless. In July 2014, he appeared on the NBC television show The Night Shift as Dr. Landry de la Cruz's father.
As of September 2015, Martinez has appeared on the NBC daytime drama Days of Our Lives as Eduardo "Eddie" Hernandez.
In April 2016 it was rumoured that A would be reuniting with his "Santa Barbara" co-star Robin Wright on House of Cards, playing her new love interest Raul in a love triangle also featuring retired baseball player Willie Upshaw
He was married briefly to actress Mare Winningham in 1981 (they divorced later that year). He married his current wife, Leslie Bryans, in 1982; they have one son, Dakota Lee, and two daughters, Devon Makena and Ren Farren.