She was born Lilian Alicia Marks in London. Discovered by the Russian impresario Sergei Diaghilev, Markova went on to dance with Diaghilev's Ballets Russes in 1924, where roles such as the nightingale in Balanchine's Le Rossignol were created for her.

It was Diaghilev who changed her name from Marks to Markova.

After Diaghilev's death, Markova was involved with such pioneering dance companies as Marie Rambert's Ballet Club, which later became Ballet Rambert, and Ninette de Valois's Vic-Wells Ballet, which later became the Royal Ballet.

She also created roles for Frederick Ashton, Michel Fokine, Antony Tudor, L_onide Massine, Bronislava Nijinska, George Balanchine, John Taras, and Anton Dolin.

In 1935, with Dolin, her partner for much of her career, she founded the Markova-Dolin Ballet in order to bring new works to ballet audiences. It was the first of several companies they would establish before founding the English National Ballet.

Markova retired from performing in 1963, and the same year became director of the Metropolitan Opera Ballet. She remained at the Met for six years, and continued to teach and to stage and direct ballets afterward.

Matz Skoog, artistic director of the English National Ballet, said in a statement, "With the passing of Dame Alicia, we see the end of an era. She was a true giant of the ballet world and the last of her generation."