elmah.io is a cloud-based error logging and uptime monitoring service for .NET web developers that monitors websites for crashes and outages, alerting users in real-time when an event happens. The service can be integrated with ASP.NET Core applications to send SMS notifications of errors using Twilio, providing instant alerts on mobile phones. To set up this integration, developers need to register for a free trial account on elmah.io and Twilio, configure the API keys and Log IDs, and modify their ASP.NET Core application's Startup.cs file to include the elmah.io integration. The integration can be tested by throwing an exception in the application, which will trigger an error log on elmah.io and send a text message to the configured Twilio phone number. This setup provides a valuable tool for developers to monitor their website's performance and respond quickly to errors, ensuring the reliability and uptime of their applications.