Pussy Riot is of course the Russian performance art group (not really a band) who staged guerrilla performances to protest Putin's government. Unfortunately, they crossed the line when they chose to perform in an Orthodox church and were arrested. The film picks up after their arrest and follows them through the end of their trial. They do a nice job in the film discussing the backgrounds of the three who were arrested.
One thing that is not approached in the film is the rest of the group. There were four at the performance where they were arrested, and eight at the previous performance, and others who helped them write the songs and plan the performances. None of that is touched on in the film, probably because some are in hiding and apparently have fled Russia for fear of arrest.
Nonetheless, if you have even a passing interest in the subject, I would highly recommend watching the film. Although there is no original footage of the three arrested group members, the film includes plenty of interviews with relatives and a good amount of historical perspective, along with footage from the trial. If for nothing else, the closing statements of the three group members are worth listening to. It will remind you of the real definition of freedom.