If, in addition to open compressed files, you need a rock solid file manager, look for 'File Storage' on the App Store.

Pictures (jpg/jpeg, png, tiff, gif, bmp.

Documents (pdf, doc/docx, xls/xlsx, ppt/pptx, pages, numbers, keynote, txt, htm/html.

Send/receive files in real time using the iTunes File Sharing (over WiFi or using a USB cable).

Save photos and videos to the Camera Roll.

Open password-protected ZIP and RAR files.

Extract files to view or edit in third-party apps.

Use the built-in viewer for common files.

Browse and view the contents of compressed files on the fly without having to uncompress the entire archive.

Accept compressed archives from any other app, including Mail, Safari, and Dropbox.

However, in case you are intrigued to know about the other methods as well, have a look at these options below.Extract the contents of ZIP, RAR, 7-ZIP, and TAR compressed files directly on your iPhone, iPad, and iPod Touch. That is all you will require to proceed with unzipping your files without the need for a third-party app. The “Preview Content” screen shown in iOS 12 or below, or when you open a ZIP file from within another app

Finally, you need to tap on Add to the upper right to save the file to the designated folder. Next, extract your file to a suitable folder.For instance, iCloud Drive, On my iPhone, or On my iPad if you’re working on an iPad.

Once done, tap on the locations of your choice on your iPhone.

You can then scroll down to find and tap the Save to files icon.

Otherwise, towards the top-right, click the Share icon.

To preview the contents within ZIP file, you can tap on Preview Content.

Open the Files app and locate the ZIP you’ve just downloaded.

That being said, if you’re trying to open a ZIP on iOS 12 or below, here’s what you need to do: The contents of the ZIP file’s extracted folder

How to open 7z files on iphone