A problem today for Anarchism, is that it has been painted as the neo-west version of Anarchism. One of Black Blocs, and teeming with destructive youths. While the real system of Anarchism is not really about destruction of property, but collective ownership of it. It is about destroying the institutions which control our lives, not physically but ideologically and practically, so that it is the people who are in control. Not unelected elites with masses of unseen power.
It is truly a brilliant political ideology, and really hasn't been properly tested as one. It came close in the Spanish Civil War, but this conflict had too many competing ideologies on one side against the fascists, that it was undermined by the communists when it was just starting to show its worth.