iMazing - iMazing lets you transfer music, files, messages, apps and more from any iPhone, iPad, or iPod to a computer, Mac or PC. Manage and backup your iOS device simply without iTunes. (was DiskAid)
oandbackup - Make backups of selected apps on your device and restore from those backups.
checkra1n - Jailbreak for iPhone 5s through iPhone X, iOS 12.0 and up
Titanium Backup - Titanium Backup is a very old backup app that has been around since the early days of Android. In fact, it's one of the few apps that covers all versions from 1. Read more about Titanium Backup.
Blackra1n - (This is an OUTDATED jailbreaking method.)
PhoneDog Phone Transfer - Transfer data from iPhone, Android, iOS, and Computer to Anywhere without any loss with FoneDog Phone Transfer. Such as photos, messages, contacts, music, etc.