One of the most common complaints with iOS devices is the relatively low internal storage.
There are a few ways to expand storage that you may not have tried. All of these methods will cost you money, but they're cheaper than buying a new iPhone or iPad.
Wireless hard drives
Wireless hard drives that you can connect to your iOS device via Wi-Fi.
The drive broadcasts its own Wi-Fi signal like your router does, so you'll need to connect to that Wi-Fi network on iOS via Settings > WiFi. You can then access contents of the hard drive via a free.
This way to expand the storage on your iOS device is rather limited, but its portability makes it worth considering. There are some thumb drives in the market that you can plug into the iOS device to expand its storage.
The thumb drive will occupy your iOS device's charging port
Manufacturers such as Mophie make iPhone cases that double up as battery packs. The Mophie Space Pack is a case that lets you protect your phone, charge it, and also doubles up as file storage space. It works just like the thumb drives mentioned above by letting you access files through your iPhone's Lightning port.
The problem is that these cases are bulky.
Cloud storage services are the obvious answer to those worried about low internal storage on iOS devices. Poor Internet connectivity prevent cloud storage from becoming a reliable alternative to the methods mentioned above.
Flickr lets you store up to 1TB of photos and videos for free, while Dropbox or Google Drive offer 1TB storage for $10 per month.