Despite being tagged in posts, you don't get notifications. I think this would be a great feature to add so people can see when people are posting something like art made for them or by them. It would increase interactions on the platform too.
As for push notifications, we currently don't get a message sent to our emails or phones when we get a notification, meaning if we don't check the app/site itself, we won't be aware of any activity. Of course, push notifications shouldn't spam you for every like, follow or share. Using some sort of grouping method should make it so the spam is heavily reduced. Example
1 push notification per post/comment on any likes + shares
1 push notification for a comment
1 push notification for a share that has additional comments.
1 push notification for any follows.
A set timeframe between push notifications would also be a good idea to recude the spam.
I would like to be able to call a given account's attention when I @ them in their general notifications, as it is difficult to ask questions of others that I'm not already personally involved with otherwise.
Seconding @-notifications. This serves two very big functions, IMO:
I wouldn't personally use push notifications, but it seems like that would be useful for some users and I have no opposition to it. (These should maybe be separate feature requests.)