I have a MacBook Pro (Retina, 15-inch, Mid 2015) (macOS Mojave 10.14.6) and an iPhone 7 (iOS 12.4.1).
I downloaded an ebook from the internet, and started reading it on my MacBook.
A few days later I copied it onto my iPhone (using iTunes on my MacBook when my iPhone was connected).
I thought bookmarks would sync between the two devices, so I could continue reading on one device from where I left off on the other.
Unfortunately that isn't happening.
How can I keep my two books in-sync?
While reading position sync to macOS is not supported, literal bookmarks (bookmark icon) do sync between iOS and Mac over iCloud. So if you don't mind modeling the analog world, you can set a bookmark when you stop reading on one device and go to it on the other. It can take a minute or two to sync, as is typical with iCloud.
On the Mac side, turn on Books in System Preferences > Internet Accounts > iCloud > [Options...]. Then in the Books app on the Mac, in General Preferences, check "Sync collections, bookmarks, and highlights across devices".
For the iOS side, see Udhy's answer.
Reference: iPad User Guide (iOS 15.4) (in Books!), tested on macOS 11.6.5 (Big Sur)
To control some settings of Apple Books on your iOS device, you need to have iCloud Drive turned on: Go to Settings > [your name] > iCloud and turn on both iCloud Drive and Books. Then go to Settings > Books.
Under Syncing, you can change settings like these:
Turn on Reading Now to sync your reading progress, current book, notes, and bookmarks using your iCloud account. Reading Now only syncs to other iOS devices, not your Mac. Turn on iCloud Drive to sync PDFs, EPUBs, and books created with iBooks Author that you didn't purchase from the Book Store that you added to your Library across all of your devices.
Under Allow Books To Access, turn on Cellular Data to stream books while your iPhone or iPad is connected to the Internet via a cellular connection and using cellular data.
You can also change settings in the Books app. Tap Reading Now, then tap the Profile icon or your picture in the upper-right corner. From here, you can redownload your purchases, access Family Purchases, and redeem gift cards or content codes.
With Apple Books it is not possible to sync reading progress between iPhone and a Mac.
The Apple Books "Reading Now" feature only works on and between iOS devices and not between iOS and MacOS.
