Any and all messages, ranging from private correspondence with your friends to event rewards and system messages will be contained within your Inbox. A set of filters and categories are in place to help you out distinguishing quickly battle reports from gather ones and tools will allow you with a single press of a button to read all and collect their rewards if any exist or delete a bulk of messages.
NOTE: You can't delete messages that contain rewards. The rewards must be collected first. This is done to ensure you don't delete accidentally something you may wish to get first.