The Messages application on your iPhone receives all incoming SMS and MMS messages. This application also stores all messages until you manually delete an individual message. By default, the application will automatically sort all of your messages by the date your iPhone received the message. Therefore, by accessing the list of messages within the application, the messages will appear in chronological order.
Tap the "Messages" icon on the home screen of your iPhone. The messages will automatically appear in a summary list organized by the date of the message.
Scroll down to search through the messages in chronological order. The newest message will automatically appear at the top of the Messages application and as you scroll down you will find progressively older messages.
Tap an individual message to open the detailed message thread.