We explored how to build a custom chat widget in a Vue app using Daily's sendAppMessage method, which allows sending messages to anyone in the call. We demonstrated three main steps: sending messages with `sendAppMessage()`, receiving and displaying messages with an event handler, and displaying messages in the Chat UI by passing the messages array as a prop from Call to Chat. The chat widget can now send, receive, and display all messages, and we discussed its limitations and potential applications beyond just chat functionality.