The iOS 11.4 update finally brings Messages in iCloud, which means you can treat your iMessages like you treat your photos.
Your messages will sync across all iOS devices and should work soon on Mac. (Update: It works on Mac now, once you update to macOS 10.13.5). You can even delete them from an iPhone or iPad that’s short on space. But they will remain accessible from the cloud. Here’s how to switch on iCloud support for Messages.