1. A method for execution by a wireless user device to process SMS messages, the method comprising: automatically grouping a plurality of individual SMS (Short Message Service) messages into threads, each thread containing one or more messages between a respective pair of two addresses comprising an address of the wireless user device and another address, wherein each SMS message is grouped into one of the threads based on the another address of the SMS message; for each thread, displaying a respective UI (User Interface) display element representing the thread; receiving a selection of a UI display element representing a particular thread; and performing an individual function upon each of the individual SMS messages of the particular thread; wherein individual functions available comprise a thread open function, and performing the individual function respectively upon each of the individual SMS messages comprises displaying in a conversation history display listing each of the individual SMS messages of the thread.