How to make remote incremental backup of LUKS-encrypted disk/partition

Some of us have our hard drives at home or on a VPS encrypted by Linux Unified Key Setup (LUKS) for security reasons, and these drives can quickly grow to tens or hundreds of GBs in size. So while we enjoy the security of our LUKS device, we may start to think about a possible remote backup solution. For secure off-site backup, we will need something that operates at the block level of the encrypted LUKS device, and not at the un-encrypted file system level.