How to check my iCloud text messages? Can anyone tells me how to view my text messages on iCloud? I know that iCloud will back up my messages on my iPhone 5S, and I am very curious about checking the iCloud messages. Is there any solution?
You can only access your messages on an iOS device or on a Mac with the Messages app. You cannot access the messages through iCloud.com on the web. 

Mac Basics: Messages helps you chat instantly
http://support.apple.com/en-us/HT202549