Wordnik migrated their live application from MySQL to MongoDB to address scaling issues. They moved over 5 billion documents totaling over 1.2 TB of data with zero downtime. The migration involved setting up MongoDB infrastructure, designing the data model and software to match their existing object model, migrating the data, and optimizing performance of the new system. They achieved insert rates of over 100,000 documents per second during the migration process and saw read speeds increase to 250,000 documents per second after completing the move to MongoDB.