Developing cross-platform mobile applications with Ionic and connecting to the Vonage SMS API allows for sending SMS messages, enabling businesses to communicate efficiently. To start building this application, one needs an IDE like Visual Studio Code or Sublime Text, Node.js, a Vonage API account, and the necessary packages such as `@ionic/angular` and `@hapi/hapi`. The process involves creating an Ionic application using Angular, installing the required packages, configuring the HttpClient, and building a basic UI. Additionally, a back-end server is created using Hapi to handle incoming requests from the client-side application. To overcome CORS issues during development, one can modify their hosts file to re-route HTTP requests to localhost. Once both the front-end and back-end are set up, they can be run concurrently in separate consoles, allowing users to send SMS messages using test numbers provided by the Vonage dashboard.