Albright won the silver medal at the 1952 Olympics. She won her first World title in 1953, silver in 1954, a second gold medal in 1955, and her fourth medal, silver, in 1956.
In 1956, while training for the Olympics, Albright fell due to a rut in the ice and cut her right ankle joint to the bone with her left skate. The cut was stitched by her father, a surgeon. At the 1956 Winter Olympics in Cortina d'Ampezzo, Italy, she became the first American female skater to win an Olympic gold medal.
Albright retired from competitive skating after 1956 but has maintained a prominent role in the figure skating profession as a member of the Executive Committee of the U.S. Olympic Committee.
A graduate of The Winsor School in Boston, Albright entered Radcliffe College in 1953 as a pre-med student, and focused on completing her education after the 1956 Olympics. She graduated from Harvard Medical School in 1961, went on to become a surgeon, and she practiced for 23 years, continuing as a faculty member and lecturer at Harvard Medical School. For a while she chaired the Board of Regents of the National Library of Medicine at the National Institutes of Health. As a director, she has served both not-for-profits such as The Whitehead Institute for Biomedical Research and the Woods Hole Oceanographic Institution and for-profit enterprises such as West Pharmaceutical Services, Inc., and State Street Bank and Trust Company. She is currently the Director of the MIT Collaborative Initiatives.
Albright was married to Tudor Gardiner, a lawyer, from 1962 to 1976. In 1981 she married former Ritz-Carlton hotel owner Gerald Blakeley, who shares her association with Woods Hole and is chair of The Morehouse School of Medicine.