At one point they used to have a little notification at the top-right, on your profile pic, to tell you that you had a reply, or whatever.

I'm honestly not sure where that went.

These days I mainly just monitor my steemd page to see if I've received comments, upvotes, etc.

busy.org might have a better notification system - I haven't checked it out yet, to be honest. Mostly I'm trying to avoid using apps that sit on top of the blockchain, other than steemit, because they tend to take a chunk of your author reward.