My son was throwing horrible tantrums as early as 9 months, And while when they're older and have verbal skills nailed down (some kids it's as early as 18 months, mines still working on it at 2) a lot of tantrums are from frustration at not being able to get their point across about something. I liken it to my step-father (his first time around a baby)as trying to reason with a telemarketer who won't stop calling you. They're just doing their job trying to get you to buy their products (you're just trying to get him to clean up his toys/eat his veggies whatever), and you just want them to leave you alone.
The only thing that makes my sons tantrums stop, is by telling him "I don't want to talk to you when you're screaming at me, and throwing things" and walking away from him. It still goes on for another couple of minutes, but soon calms down. Maybe this will work for you as well?