Alfredo Rodríguez Salicio was born on October 7, 1985, in Havana, the older of two sons of the singer, songwriter and television presenter Alfredo "Alfredito" Rodríguez and Mayra Salicio. He began formal music study at seven, wanting percussion, but was made to wait until ten to choose an instrument and picked piano. His schooling was classical, at the Manuel Saumell Conservatory, the Amadeo Roldán Conservatory and the Instituto Superior de Arte, while he learned popular styles on the bandstand: from the age of fourteen he played in his father's orchestra and wrote arrangements for boleros, rock and roll and dance music. At fifteen an uncle gave him a copy of Keith Jarrett's The Köln Concert, his first encounter with improvised music, and he turned toward jazz. He won an honorable mention at Cuba's JoJazz competition for young jazz players in 2003, and by 2007 he was leading a trio with bassist Gastón Joya and drummer Michael Olivera.

In 2006 he was chosen as one of twelve pianists to play at the Montreux Jazz Festival in Switzerland. At a gathering at the home of the festival's founder, Claude Nobs, he played for Quincy Jones, who said he wanted to work with him. It took three years to make that possible. In January 2009, after engagements in Mexico with his father, he left Cuba, carrying, in his words, a suitcase with a sweater, a pair of jeans and his music; he was granted political asylum at Laredo, Texas, and settled in Santa Monica, California, with Jones as his producer and mentor. Jones, who died in 2024, co-produced or executive produced his albums through 2019. Rodríguez is also credited as a co-writer, with Jones, the composer Tan Dun and the singer Siedah Garrett, of "Better City, Better Life," the official theme of the 2010 Shanghai World Expo.

He signed with Mack Avenue Records in 2011, and his first album for the label, Sounds of Space, appeared in March 2012. All eleven pieces are his own, and Jones co-produced it. Alongside Joya and Olivera it features the bassist Peter Slavov and drummer Francisco Mela on two tracks, the reed player Ernesto Vega, and a woodwind and horn quartet on the closing "Fog." The Invasion Parade (March 3, 2014) took its name from the carnival procession held each year in Santiago de Cuba, and turned his memories of the island into nine tracks that mix originals with "Guantanamera," María Teresa Vera's "Veinte Años" and "Quizás, Quizás, Quizás." Guests included the bassist and singer Esperanza Spalding and the percussionist and singer Pedrito Martinez. His arrangement of "Guantanamera" was nominated for a Grammy Award for Best Arrangement, Instrumental or A Cappella, at the 57th Annual Grammy Awards in 2015.

Tocororo (March 4, 2016), named for a Cuban bird said to die of sadness in captivity, took up his experience of life outside Cuba after seven years away, with guests including the bassist Richard Bona, the duo Ibeyi, the trumpeter Ibrahim Maalouf and the singers Antonio Lizana and Ganavya. The Little Dream (February 23, 2018) pared the music back to a trio with the guitarist and bassist Munir Hossn and Olivera, and he performed as a trio on an NPR Music Tiny Desk concert released in October 2018. Since 2017 he has also worked as a duo with Martinez, which produced Duologue (February 1, 2019, Mack Avenue), recorded in Los Angeles from May 29 to June 1, 2018, with Jones as executive producer.

He moved to Miami in 2019 to be near family, and wrote most of Coral Way (August 18, 2023, Mack Avenue) at home over about three years. It is his first self-produced album and carries guest appearances by the Madrid-based singer Alana Sinkëy and the Cuban funk artist Cimafunk. In a different direction, ¡Take Cover!, released on January 23, 2026, on Take Cover Records, is an eleven-track set of reinterpretations, among them "Oye Como Va," "Hotel California" with Martinez, "Entre Dos Aguas" and "La Cucaracha," played by a trio with the bassist Yarel Hernández and Olivera. He also tours in a trio with Bona and Olivera that played Jazz à Vienne in 2021 and the INNtöne Jazzfestival in 2022; as of November 2026 the trio is listed for a concert in Oslo on November 18.

Rodríguez combines conservatory technique with the rhythms of Cuban popular and folk music: on The Invasion Parade he worked with the conga santiaguera of eastern Cuba, Afro-Cuban rhythms and música guajira, and he writes arrangements across idioms, a habit from his years in his father's band. His entry into improvisation came through Keith Jarrett, and early reviewers heard in him a mix of Bill Evans, Kenny Werner and Fred Hersch, with touches of Thelonious Monk in his ideas, a sparse-to-dense piano language of angular runs, thick harmonic clusters and sudden lyrical turns. NPR's review of The Little Dream heard Jarrett, Jaco Pastorius and Pat Metheny in it in equal parts. His records pair original compositions with arrangements of familiar material, from Cuban standards to a timba reworking of Michael Jackson's "Thriller" on Duologue, and he has described Jones as the mentor who taught him to look for beauty in any kind of music. His later work leans toward bright, danceable ensemble sound, with Miami's Latin pop and salsa scene as the backdrop for Coral Way.