I was reading through this https://en.bitcoin.it/wiki/Scalability and wondering were the clients are with implementing the scalability upgrades?

Is every transaction with BTC recorded in the blockchain which is downloaded by every wallet?
Is all the history stored? Sounds like it....
How can this scale if millions/billions of customers start using BTC from their wallets stored on their smartphones?
Wouldn't the network get overwhelmed if every wallet/node had to be kept in sync?

Thanks