How do you handle errors specifically within Next.js API routes?

In Next.js API routes, errors should be handled by explicitly setting the HTTP status code and returning a JSON response. You can use a `try...catch` block to wrap your API logic. In the `catch` block, you would set the response status (e.g., `res.status(500)`) and send a JSON object describing the error (e.g., `res.json({ message: 'Internal Server Error', details: error.message })`). This allows clients consuming your API to understand the error and react appropriately, rather than receiving an unhandled server error.