The group, which was formed in 1985, consisted of seven musicians of diverse nationalities, and the themes of much of their music involved political and social justice, the status of immigrants and minorities in France, and the inhabitants of the French banlieues, or suburbs.

Its 1995 album, Le bruit et l'odeur ("The Noise and the Smell") took its name from a gaffe made by then-president Jacques Chirac in reference to the conditions in the French banlieues, many of which have large immigrant populations.

[4][7] As Zebda was originally formed for a community organization and many of the members met through social initiatives and activism, the band remained highly political throughout its existence.

Difference, discrimination, and exclusion are themes that feature heavily in J'y suis, j'y reste [a song from the album Utopie d'occase].

In the 2001 municipal elections, Zebda sponsored and spearheaded a list of independent candidates, Les Motivé-e-s ("The Motivated Ones"),[10] who ran for office on the platform that the current local government was not representative of all demographic groups in the city.

[4] The group of candidates, two of whom were Zebda band members, won 12.38% of the vote in the first-round elections, and advanced to the second round, where they were narrowly defeated.

[7] While the content and themes of their music are politically serious, typically detailing racism and discrimination, the group has been said to have a positive and "upbeat" sound that represents the ideal of peaceful coexistence and cultural diversity.