I leveled from 0-30 playing dom, and it was the only way I played LoL for a while. I stopped playing LoL entirely when I realized there would never be a ranked mode and only recently came back to try SR. When there was a bot to tell you your ELO, I was ~1650 which is like Gold3. I'm Silver4 in SR. (Riot removed that bot, btw)
I like it better because there's no laning phase. The amount of time that you're in a game that you know you have no way of winning is way lower than SR as well.
As far as the history:
When it was launched, there was no ranked or ladder. Riot said they'd add it when it got more popular, but lots of people were saying they'd quit since there was no ranked (I eventually did)
There was a bug for a several months for draft dominion only that meant if you dodged a match, there was no penalty. It was literally impossible to get a draft dominion game because every game would be dodged.
So, you were forced to play blind. Blind was stupid because there's no ban phase, and Kassadin was the most OP champ in dominion and the community eventually realized it. He could riftwalk over basically every wall. They finally issued a dominion-only nerf to his riftwalk this year, but that's like lolwaytoolate.
Even after they fixed the draft bug, everyone played blind because no one was in the draft queue anymore. I heard people were trying to organize to move to blind -> draft but I don't know if that ever worked out.
dominatedominion.com used to organize weekly tournies, but the website is down so that may be dead.
Wait, there are still some recent tourney videos here:
https://www.youtube.com/user/VATOCLAN/videos