Hi L.!
As with everyone else who responded, my son was exactly the same way! At this age, they understand more than they can express. So they act on their frustration. At two, my son throws himself on the floor! But at 18 months, he would throw his toys, kick, flail his arms, scream. You name it, he did it!
I really started watching how he played and learned the signs of when a tantrum would soon emerge! Sometimes, I was able to head them off, sometimes I wasn't. I usually stay with him during his tantrum, as tempting as leaving would be! I didn't want him to think I was abandoning him. However, I know moms who ignored tantrums, and that worked as well. I think it depends on your child's personality.
I never, ever give in to the tantrum. I don't try to negotiate. If his tantrum escalates to hitting or throwing toys, I always remove him from the situation. I explain to him why I took him away. I stay with him until he calms down and then talk to him about why he got upset. I ALWAYS, ALWAYS, ALWAYS acknowledge his feelings, "I know you were very frustrated because you had to share your cars." I then alo express that I cannot understand when he screams, but now that he's calm I can find out what he needs because he can use his words.
Remember to keep your cool too! Whenever I got upset or angry, his tantrums were worse. The calmer I remained, the better he recovered.
I wouldn't recommend spanking. The crime should fit the punishment. The only time I ever spanked my son is when he ran away from me in a parking lot full of cars, and he needed to know that he could never do that again. I know a mom who spanks or smacks her son's hand whenever he hits, and it does no good. He still hits and hits more frequently. My son has stopped hitting and throwing his toys. Her's has not. He still has melt downs (every toddler does), but it's not as violent! Good luck!