Pussy Riot comes with a lot of history and context. They are a Russian performance artist collective with loose membership formed in 2011. They have been engaging in activism mostly through arts, including impromptu punk shows typically performed in their iconic colorful ski masks. The group gained major notoriety after a guerilla show they put on at the Cathedral of Christ the Savior in Moscow in 2012 known as "Punk Prayer - Mother of God, Chase Putin Away!". Arrests and court cases followed, propelling members Nadia Tolokonnikova and Masha Alyokhina to prominence as the de facto public figures of the group. Pussy Riot was disbanded, but the group's activism continued. Their current incarnation is centered around Tolokonnikova and Alyokhina, along with other members who also escaped Russia. Their music is not as much punk these days as hyperpop with exaggerated pop features, though they maintain their anti-Putin, anti-fascist, and feminist sentiments.
Bikini Kill and Grlwood, for the punk Pussy Riot; Violent Vickie and The Julie Ruin for the pop one.