Twilio and SendGrid have come together as one company, sharing a customer-first mindset that values empathy for users. The author, Sameer Dholakia, built an SMS responder app using Twilio and SendGrid's services, which responds to incoming SMS messages with a personalized email containing a GIF. To build this app, developers need to sign up for both Twilio and SendGrid accounts, install necessary Python libraries, create a virtual environment, and set up environment variables for sensitive data like API keys. The app uses Flask as the microframework and sends emails using SendGrid's services. Once deployed, the app can be accessed through an ngrok tunnel, allowing it to receive incoming SMS messages and respond with a personalized email, completing the Twilio-SendGrid integration.