When you need to split the bill, try Circle Pay, a digital money-transfer system that lets people send dollars, euros or Bitcoin through iMessage. The Circle Pay app requires some setup and registration, but it works simply in the iMessage interface, and it, too, is free.

Image Chess42 is an ultraminimalist chess game playable inside iMessage.

The app iTranslate brings dynamic automated language translation to iMessage. You can chat with someone who speaks a different language and translate the conversation in real time, without having to leave the chat interface. It’s free, and it works fast and quite well, though the controls can be confusing and sometimes, as with any machine translation, the result may sound like a Spanish or Portuguese version of Yoda.

Another test of the new iPhone’s performance is how it handles games. Monument Valley, which is $4, is a highly regarded 3-D puzzle game with clean, abstract graphics and simple gameplay: You have to guide your character through an architectural labyrinth that’s part M. C. Escher, part artwork all its own. Don’t be surprised if you stop just to admire how pretty it is.

The Obscura app, at $5, lets users take full control of the photographic powers of the iPhone’s camera app. You can adjust the ISO and focus to get really creative; it’s almost like using a digital single-lens reflex camera.

Move beyond Apple’s built-in keyboard with Microsoft’s Word Flow, which is free. Get a deeper understanding of how we measure time on Earth with the lovely Cosmic Watch clock app for $4. Back up your photos and documents to the cloud with Google Drive, which is free. And finally, turn your iPhone into a capable document scanner for $4 with Scanner Pro 7.

Quick Calls

DataMan Pro is a popular app for tracking which apps on your phone are consuming the most mobile data. The app has been updated for iOS 10. It’s $6 and also works with Apple Watch.

The third-party keyboard app SwiftKey has always been popular because its predictive text features are great, but on Android, its makers have just taken the app to a new level. SwiftKey now has neural artificial intelligence, so instead of a simple suggestion algorithm, it looks at what you’re typing and tries to grasp the context of your message so it can provide better suggestions. SwiftKey is free.