Android (e.g. Samsung, HTC, Sony): To delete chat messages, tap a message in the chat for a few seconds to mark it, then tap on the trash can symbol. To delete the entire chat history, long tap on one message to mark it, then tap on the symbol next to the trash can in the top right corner. This marks all messages, and you can delete them by tapping on the trash can symbol.
iOS (iPhone): To delete chat messages, tap one message in the chat for a few seconds. Now you can choose either delete (one message) or delete all (entire history). To delete chat messages, tap one message in the chat for a few seconds. Now you can choose either delete (one message) or delete all (entire history).