Alsop went to Yale University and then got a master's degree from the Juilliard School in violin playing. She won the Koussevitzky Conducting Prize at the Tanglewood Music Center in 1989, where she studied with famous conductors such as Leonard Bernstein.
Alsop has conducted many of the world’s most famous orchestras. Since 2002 she has been the conductor of the Bournemouth Symphony Orchestra, and in 2007 she will become the conductor of the Baltimore Symphony. This will make her the first woman conductor of an important American orchestra.
Alsop has won many prizes and made lots of recordings. She has conducted and recorded many pieces by American composers, including the complete orchestral works of Samuel Barber.