There are a number of proposals. In bitcoin, sidechains (separate blockchains that get anchored to the main chain) are oft-touted, as is the lightning network.

There are a number of proposals. In bitcoin, sidechains (separate blockchains that get anchored to the main chain) are oft-touted, as is the lightning network. The idea is that only the most important / highest value transactions make it onto the main blockchain. There are other approaches as well. Most actors don't need all past transactions- just the valid spendable outputs. Old txs could be pruned. You can also apply ideas from regular databases, like sharding.