The Files app, added in iOS 11, supports zip files. You can open them, see their contents, and extract files without any third-party apps. You’ll still need an app from the App Store if you want to create zip files.
When you download a zip file in Safari, your iPhone or iPad will offer to open it in the Files app. Tap “Open in Files” to do so. You can also save zip files to the Files app from other applications.
You’ll be prompted to choose a location for the zip file. You’re saving a copy of the zip file to this location.
Select a location—like your iCloud Drive or a folder on your iPhone—and tap “Add.”
Tap the zip file in your Files app to open it.