Active or Passive, Powered: what’s in a name?

Some choices are easy: Do you want your speakers in black or white? Do you want big or small ones? Do you want expensive ones or cheap ones?  Do you want to buy them from Rapallo? (That’s a no-brainer…) But when it comes to what type of speakers you want, lately it can get a bit complicated. Most speakers are passive, but recently more and more active speakers seem to pop up. But what’s the difference? Why would you choose one over the other and what’s best for you?