[1] Founded in 1968 by Jean Mooskin and Dick Roth,[2] the school practices progressive pedagogy: classes and advisory groups are small, teachers go by their first names, and students have significant independence.

The school was named for 18th century British parliamentarian and philosopher Edmund Burke, who wrote, "When bad men combine, the good must associate; else they will fall one by one."

[5] In 2003, Burke earned city approval to expand its facilities[9] with a new building that would increase both size and capacity and now includes new computer labs, offices, middle school classrooms, athletic facilities, a theater, and an underground parking garage.

[2] In summer 2021, Burke began a renovation to the historic high school building, which resulted in a new ceramics studio, renovated space for digital and wet photography, community gathering space, new fitness center, and a lunch servery.

On April 22, 2022, a gunman armed with four rifles modified to fire on fully-automatic and mounted with scopes, along with two handguns and more than 1,000 rounds of ammunition, positioned himself on the fifth floor of an apartment building adjacent to the school.

In 2024–25, those students represent 59 different zip codes in DC, Maryland, and Virginia and 40% self-identify as people of color.

Burke offers varsity teams in Volleyball, Cross Country, Soccer, Basketball, Swimming, Baseball, Track and Field, Ultimate Frisbee, Golf, and Softball, which won three consecutive championship titles in 2017-19.