Versioned schema migrations involve using multiple files or scripts to document and apply changes to a database schema over time, functioning similarly to version control systems like Git. Typically stored alongside code, these migration files are applied incrementally using third-party tools, with a dedicated database table tracking which scripts have been executed. An example with the Laravel framework demonstrates how Artisan commands manage migrations, creating and altering database tables while tracking changes in a migrations table. Benefits of this strategy include familiarity for developers, ease of reverting changes, and straightforward tracking of incremental updates. However, drawbacks include difficulty in visualizing the entire schema at a given time and potential issues if schema modifications occur outside the migration tool. With platforms like PlanetScale, developers can use safe migrations to ensure zero-downtime and secure schema updates, leveraging branching and deploy requests to manage changes effectively.