Photo Transfer App is one of the simplest solutions I've encountered for transferring photos and videos between mobile and desktop devices -- so long as your devices are all on the same Wi-Fi network.
When you open the app on your device, it immediately asks if you want to send or receive files (only photos and videos are supported). Once you make your choice, it asks if you'll be transferring with an Apple computer, Windows computer, or mobile device (Android or iOS only). Whichever option you choose, your devices will have to be on the same Wi-Fi network for the app to work, which is a bummer, but still understanding considering the quantity and size of the potential file transfers.
For transfers between your mobile device and desktop computer, the app will give you an IP address to direct your desktop browser to. From there, you can choose which files to transfer from your mobile device, then easily download them from your desktop browser. What's nice is you can even download all the files at once in a Zip file. If you're receiving files on your mobile device, all you have to do is upload them through your desktop browser, using that same IP address.
To transfer from Android to Android, only one device needs the app installed, so long as the other can navigate to the IP address through its browser (just like the desktop process). To transfer from Android to iOS, though, both devices need the app installed. And unfortunately, transferring of video files is not supported between Android and iOS as of yet.
Overall, I highly recommend this app for anyone in need of a solution for photo transfers. Sure, you can use Android's built-in share features, but that's probably not the best choice, if you're looking at moving, say, 50 files at once. Photo Transfer App Lite (free) lets you transfer up to two files at a time, while the full paid version of the app lets you transfer up to transfer up to 200.