Your WhatsApp chats are automatically backed up and saved daily to your phone's memory. Depending on your settings, you can also periodically backup your WhatsApp chats to Google Drive. If you uninstall WhatsApp from your phone, but don't want to lose any of your messages, be sure to manually back up your chats before uninstalling. To backup your chats, go to WhatsApp > Menu Button > Settings > Chats > Chat backup > Back Up.
To export a copy of the history of an individual chat or group, use the Email chat feature:
An email will be composed with your chat history attached as a .txt document.