I haven't played a proper Pokemon game since the second gen games on a GBC, and I was wondering if there's a modern game that you can play on a computer/phone and connect via internet to do trades/battles etc.

I'm talking about a proper game with the quests and gym challenges and story, not just that site where you create a party and then have battles. I want the whole Pokemon experience with training and evolutions etc.

Does this exist on a computer/android platform?