I have a 20 month old boy and overall he is a sweet child, but at about 16 months or so I found the same thing happening that you mentioned, screaming throwing himself on the floor. I had read in the book "Your One Year Old, Funloving and Fussy" by Loisa Bates that age 15 -21 months is a hard age and they will have more temper tantrums; this book helped me emensly over all, I think at about 1 year he started acting in ways I didn't like, and the book helped change my perspective to be more realistic as to how a 1 year old should act (I'm a 1st time Mom), I was expecting him to act like a 2 yr old.
I found that if I try and guard his sleep (I use "Healthy Sleep Habits, Happy Child" by Weissbluth to help me figure this out) that he doesn't have as many tantrums. He is also picking up sign language very quickly lately (I use the "Signing Time" videos, he is a hearing child, but sign language is one way to cut down on tantrums and we have found it works more and more each day as he understands the signs more). When he does have the tantrums, I run through my mind if he is hungry or needs to go down for a nap, etc . . .if none of these things are needed then I just ignore him for a few mins then try and distract him (I'm sure you already do this, but I was just trying to be specific). He also hits his head at times along with these tantrums, that is when I definitely know he needs to sleep.
So I hope you find what works for you, I know how frustrating it can be.