The first solution was to simply increase the amount of data that the blockchain could store. Increase the block size limit to double the number of transactions possible.
It was a simple solution with a simple flaw: when it ran out, you had to start over. If this continues, the amount of storage required to hold the blockchain will spiral out of control, rendering ordinary users unable to run the Bitcoin software in their own homes.
Another option was to reduce the amount of time required to create a new block. The issue with this is that a confirmation period is required to confirm the validity of new blocks. In less time, you could create 100 new blocks before you even realize that there's an issue.