Apparently there are 3 “solutions” for the blocksize problem trimming, sharding and lightweight wallets.
Trimming is apparently a way of making the blocks more efficient in terms of how much size they require, from my understanding it’s a way to make the blocks smaller while letting them handle the same load.
Sharding is a process by which not all wallets require a full blockchain of some sorts, apparently this should make the blockchain smaller as well as make the network faster.
Lightweight wallets are similar to other wallets we know that don’t require the block chain to operate.
I haven’t really looked into it properly so I’m afraid I can’t offer much more than a small basic understanding.