While the native Files app on iPhone and iPad is good enough for certain users, it certainly doesn’t please most iOS users. The reason is that Apple doesn’t allow users to access the internal file system. That means while there is a Files app on your device, it is next to useless when it comes to managing your device’s internal files. If that is what you want to do, you will be better served by third-party file managers for iPhone which you can find on the App Store.

Documents by Readdle
The Documents app is best-known for its user-friendly menu system: Just select files, and use the menu button to see all possible operations (of which there are many). The app also makes it easy to unzip, rename, and move multiple files and folders.
This is tagged as the super app for iPhone & iPad. Read, listen, view, annotate almost anything you want on your iPad and iPhone. Files, documents, books, any content is at home in Documents by Readdle.
Among the top features are: Import and Save Files, Manage with Color Tags, Integrate with Cloud Services (such as iCloud, Dropbox, and Google, etc.), Password Protect files, Read and Edit PDF documents you send and receive.
Download Documents App
Free to download and use basic features
Documents Plus $12.49, or Professional PDF Editor for $49.99

File Manager & Browser
File Manager is a FREE file manager and virtual USB drive for the iPhone and iPad. Easily view images, audio, videos, PDF documents, Word documents, Excel documents, ZIP/RAR files, and more. Top features include PDF Reader, Microsoft Office, Excel, Powerpoint support, Integration with Cloud services (such as OneDrive, Dropbox, etc), Music Player, Copy, Move, and Zip Multiple Files, Passcode protect files and many more.
This is an ad-supported file manager that provides all the basic features for free.
Download File Manager & Browser App
Free to download and use basic features

Total Files
If you’re looking for a heavy-duty file manager—something focused on helping you manage files in a visual way—Total Files might be for you.
The app doesn’t distract with add-on features like VPNs or PDF editing. It gets right down to the business. The app opens to the Local Archive, where you’re free to add new folders and import files. You can go to the Clouds section to link cloud storage like Dropbox, Google Drive, or more.
While you can’t link iCloud Drive here, the app has a handy import feature that will move any file from the Files app (local or iCloud Drive) to the Total Files directory. The app also features banner ads, but you can remove them by unlocking the complete app for $4.99.
Download Total Files App
Free to download and use basic features
Upgrade to remove ads: $4.99

GoodReader
If you deal with a lot of PDFs for work, you should consider using a separate app for managing all your PDFs—and GoodReader is as good as it gets.
It offers a full-blown file management system for your PDFs, allowing you to organize them in multiple folders and move them around with ease. You can also connect to cloud storage services like Dropbox, OneDrive, Google Drive, and more. This lets you download, upload, and sync changes to existing PDFs without switching over to a different app.
First released in 2009, GoodReader® is truly a veteran of the App Store.
Download GoodReader App
$5.99 to Download

Microsoft OneDrive
If you use a Windows PC for work, or at home, chances are all your files are already saved on Microsoft OneDrive. And why wouldn’t you? You get 1TB of storage space with your Microsoft 365 plan anyway.
But if you use an iPhone or an iPad, your experience of using OneDrive in the Files app is less than ideal. That’s why you might want to use the OneDrive app itself. It’s quite good, and it supports the usual file management features that you want. You can import, move, export, and unzip files with ease.
Download Microsoft OneDrive App

Files Pro
Files Pro is one of the best document viewer apps available on the app store. With Files Pro, you can store and view your documents transfer them quickly from any Mac or PC.
What’s more interesting is that the Files Pro seamlessly integrates with cloud services like Box, Google Drive, OneDrive, Dropbox, etc. The app also provides users a web browser that can be used to download any files or documents.
Download Files Pro App
$2.99 to Download
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What’s a good file manager to organize machine embroidery files?
Documents is the best I have used for organizing anything! I have used others, including ones mentioned in this article, but I have found Documents being the best for ease of use and visual simplicity.