Photos also helpfully collects all your sharing updates in a special Activities album in Shared view in both Photos for Mac and iOS. This album houses big, beautiful thumbnails of the most recent additions to each shared album, as well as comments and likes--it's a great way to breeze through shared content to see what everyone is up to.
In order to edit or use a shared photo in projects of your own, you need to download it. On your Mac, Control-click a thumbnail and choose Import from the shortcut menu. Photos dutifully adds the item to your Last Import album, where you can treat it like any other picture or video in your library: Edit it, add it to another album, include it in a project, and so on. To download content in Photos for iOS, tap the image thumbnail to open it, tap the share icon that appears, and then tap Save Image from the row of icons that appears at the bottom of your device's screen.
Letting subscribers add content
A bonus (and semi-hidden) feature of shared albums is that you can let any subscriber add their own pictures and videos to the album. This creates an incredibly convenient, two-way sharing between you and your subscribers. To set it up in Photos for Mac, double-click a shared album to open it or, if you have the sidebar turned (Option + Command + S), just click the album's name in the Sharing section to select it. Next, click the subscriber icon in Photos'toolbar (circled below). In the sheet that appears, turn on Subscribers Can Post.
To do this in Photos for iOS, tap Shared at the bottom of your screen and, if necessary, tap the Back button at upper left to close the shared album you're viewing so you see thumbnails of all shared albums. Next, tap the album you want to grant uploading permission to--you'll see the album's thumbnails (shown below at left). Tap People at the bottom right and in the next screen (shown below at right), tap the Subscribers Can Post switch to turn it on.
From this point on, the shared album synchronizes everyone with access to it: Any items you, or a subscriber, add to the shared album is sent to every device of every person who subscribes to it. Likewise, any items you (or a subscriber) remove from the shared album disappear on all subscribed devices (you can only delete items you yourself add). Heck, PC users can join the iCloud Photo Sharing party by installing iCloud for Windows. (For info on how to download it and set it up, visit Apple's support page.)
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