To receive and reply to SMS messages with TypeScript and Twilio, you can build an Express application that listens for incoming webhooks from Twilio. You need to install the necessary dependencies, including Express, Twilio, and TypeScript, and set up a configuration file to store your port number. Then, create a route for handling incoming webhook requests using the Twilio package's MessagingResponse class to generate TwiML. To connect the application to a Twilio phone number, you need to access the application from a public URL using ngrok. Finally, you can use TypeScript types to define the shape of your request and response objects, making it easier to catch errors and ensure type safety in your code.