At the time of studying at C.U.E.C, he met Maria Eliizondo(an actress and a writer). He had his first son, Jonas Cuaron with her. However his time at the university was short-lived as he was expelled because of constant disagreement and arguements with the teachers at the university. To support his family he went on to work in a museum. He got an offer from Jose Louis Garcia Agraz who was visiting the museum to work as a cable person in the movie' La Vispera(1982). That proved to be the turning point in his career. In 1984 he was the assistant director in the film Nocaut. He was also assistant director for several Latin American film productions including Gaby; A true story and the movie Romero.
Cuaron's first feature film produced in the United States was: a little princess (adaptation of Frances Hodgson Burnett's classic novel). His next feature was an adaptation of Charles Dickens Great Expectations. His next project was the controversial comedy film Y Yu Mama Tambien. The film was an international hit. It got favorable reviews from the critics and also landed Cuaron an Academy Award nomination for Best original screenplay with co-writer and Blrother Carlos Cuaron. Cuaron's feature children of men received wide critical acclaim. The film landed Cuaron three Academy Award nominations. In 2003, Cuaron directed the film Harry potter and the prisoner of Azkaban. It received favorable reviews from the critics as well as the author of the Harry potter series , J.k.Rolling. Until the release of harry potter and the deathly hallows-part 2 it was said to be the most critically acclaimed film of the harry potter film franchise.
During the promotion of the film, Y tu Tambien in venice Alfonso met cinema critic Annalisa Bugliani, and began dating her in 2001. They got married in the same year .They have two children: daughter Tess Bu Cuaron and son Olmo Teodoro Cuaron. The couple got divorced in 2008. Since 2010, He has been in a relationship with Sheherazade Goldsmith. He has a net worth of 20 million dollars.