iOS 13 finally adds support for zipping files and unzipping compressed files. You could do this before with third party apps but it's about time native support was added, especially since they introduced a file management system (Files) in iOS 11. Here's how to open and extract zipped files and how to compress your own files and folders on iPhone or iPad running iOS 13 or better:

Unzip

iPhone's screenshot feature received an update with iOS 13 - the ability to capture an entire Safari webpage in one shot. A full page or "scrolling" screenshot is saved as a PDF though, so it isn't technically a new ability, as you could do this prior to iOS 13 with the "Save as PDF" Share menu option. This makes it more convenient though, and gives you instant access to the screenshot's markup tools so you can quickly highlight, circle or cross out text, add notes and more.

Here's how to take a full page screenshot on iPhone and iPad: