Delgado was born in Calexico, California to Emilio Delgado and Carmen Rodriguez Delgado on May 8, 1940.

He was raised in his grandparents' house in Mexicali, Mexico, with his poor extended family. As a citizen of the United States, he would walk daily to attend a public school in Calexico. He began working odd jobs as a ten year old, and at his uncle's bicycle shop at age 12. His family moved to Glendale, California when he was a teenager. During high school, three years of which he attended Glendale High School, he became president of the Thespian Club, played trombone both in their orchestra and a jazz band, and was a drum major in the marching band.

Delgado began acting professionally in 1968, after nine years of "trying to knock doors down in Los Angeles to get in." That year, he received his first Equity job in a summer stock play starring Martha Raye, and later was cast in the first Mexican-American soap opera, Cancion de la Raza.

Befriending actor Sergei Tschernisch at Los Angeles Theatre company Inner City Repertory, Delgado learned of the new theatre program at CalArts, led by Provost Herb Blau. While already a professional actor as of his 1970 enrollment, Delgado praised Blau's methods, suggesting his avant-garde method was "amazing."

As of 1970, he was the artistic director of the new Mexican-American Centre of Creative Arts, which taught Chicano high school and college students from the basement of the Euclid Heights Community Centre in East Los Angeles. Delgado told the Los Angeles Times: "We are 100% positive in our approach, and we are uncompromising in our belief that our kids will come away thinking of themselves as artists. Nothing is going to stop us from attaining our identification in American society."

Delgado had a guest role in an October 1970 episode Storefront Lawyers, before being cast as a series regular in Angie's Garage, in November 1970. The new children's series focused on serving Mexican-American children. He was billed as a singer-guitarist. He speculated that Sesame Street producers discovered him through the series.

Delgado was able to do voice over work, both with and without an accent.

The enormous popularity of Sesame Street created a barrage of groups providing input on the curriculum in its second season. During the season, the program attempted to teach Spanish to children whose mother tongue was English. Producer Jon Stone told The Pittsburgh Press that their attempts were "a disaster. It was tokenism at best, and condescension at worst." For the third season, the show rebooted their efforts, adding Puerto Ricans and Chicanos, and creating new Spanish segments. Seven new cast members were added at the start of the season, including Delgado, Panchito Gómez, Raul Julia, and Sonia Manzano. Delgado was still enrolled at CalArts, as of casting. Delgado's character, Luis, ran "The Fix-It Shop," a repair service on Sesame Street, alongside Julia's Rafael. The character has been described as the "antithesis" of the Mexican and Latino stereotypes that proliferated television at the time, as he was "an honest, upstanding, hard-working, affable person." Delgado expected the role to last one or two seasons.

Delgado joined the series' live events by at least 1972, when he performed with the Jackson Symphony Orchestra.

Delgado was named the coordinator of the Children's Television Workshop's Bilingual Task Force, and sent across the country to meet with groups. The efforts were to lead to further updates to content in season 4. He would comment in 1972 that the series didn't "teach Spanish, we teach in Spanish."

Delgado is believed to have played "the same role on U.S. television longer than any other Mexican-American actor," according to CalArts.

During Sesame Street's 19th season, first aired in 1988, Delgado's character Luis became engaged to and married Maria, played by Sonia Manzano. According to Delgado, "to this day, there are fans out there who want to believe that the Luis and Maria wedding episode in 1988 was real, "but the fact of the matter is, it was just terrific acting."

Delgado later appeared at various pop culture conventions, often under the brand "Humans of Sesame Street". Delgaldo also reprised the role of Luis in the TV special Sesame Street's 50th Anniversary Celebration.

Delgado also performed in live shows throughout his Sesame Street career, singing the songs of Sesame Street and entertaining thousands of children and their families.

On Sesame Street, his character, Luis along with Raul Julia as Rafael, were the first human additions to the original cast. Luis was a handyman and an aspiring writer, who debuted on the show in 1971 simultaneously with Raul Julia as Rafael. Together they ran the L&R Fix-It Shop until Julia left the show after one season, and Luis ran the Fix-It Shop alone from then on. In season 19, Luis fell in love with Maria, performed by Sonia Manzano, and married her. The characters Luis and Maria taught viewers about Hispanic culture and language throughout their shared run of the show.

Delgado would take guest roles on other series, while Sesame Street wasn't taping. Notably, he had a recurring role as national news editor Rubin Castillo on the television series Lou Grant.

Delgado starred in the Alley Theatre production of Octavio Solis' Quixote Nuevo (2020), a modern Chicano adaptation of Don Quixote.

In Los Angeles, he was a company member of Inner City Rep, The Group Repertory, and LA Repertory. Some of his New York City theatre credits include Floating Home (HExTC), Boxing 2000 (Richard Maxwell NYC Players), Dismiss All the Poets (New York Fringe Festival 2002), Nilo Cruz's adaptation of A Very Old Man with Enormous Wings (Shakespeare Theatre of New Jersey), Dinosaurios (IATI), Night Over Taos (INTAR Theatre) an adaptation of How the García Girls Lost Their Accents (Round House Theatre), and Emilio appeared in the role of King Claudius in Asolo Repertory Theatre production of Hamlet, Prince of Cuba, with alternating performances in English and Spanish, where one reviewer wrote that Delgado "is equally brilliant as King Claudius".

His other television appearances include House of Cards, Law & Order, Law & Order: Criminal Intent, and Law & Order: Special Victims Unit. He was a regular cast member of Lou Grant and the short-lived Born to the Wind. He also appeared in episodes of Police Story; Hawaii Five-O; and Quincy, M.E.

Delgado's other creative endeavor was to sing and record with the band Pink Martini. He performed with the band at Carnegie Hall and Town Hall in New York City, The Hollywood Bowl in Los Angeles, in Woodinville, Washington at the Chateau Ste. Michelle Winery, and in Portland, Oregon at the Arlene Schnitzer Concert Hall, Crystal Ballroom and the Oregon Zoo. He appears on their album Splendor in the Grass, in which he recorded the song "Sing", a duet with China Forbes.

Buenas Noches Sr. Delgado

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Tony Figueroa