Your inbox lists everything that happened while you were away: replies, mentions, invites, reactions, asks for a bridge, new subscribers and more. Unread notifications come first, in bold, newest at the top. The ones you have seen sit below them in lighter type.
Where to find it: Click Inbox in the left sidebar, or tap it in the bottom bar on a phone. You can also go straight to your inbox. It shows a small count when you have unread items.

Tabs
All shows every notification, including invites, requests and reminders. Mentions holds replies to you and posts or comments that mention you. Activity holds trust and reactions on your stuff: uptrusts, votes, reactions, bridges and RSVPs. Each tab shows how many unread items it holds.
Acting on a notification
Click a notification to open what it points at. That marks it read, and it stays where it was. When you come back, the inbox is where you left it, with that row lit for a moment.
Some rows have a button for the next step: Reply, Vote, RSVP, Uptrust back and so on. Accept joins a group right from the inbox. The button stays until you have done it, even after the row is read.
On a computer, point at a row (or move to it with the keyboard) to see Mark read and a ⋯ menu. The menu can mark it read, Mute this post so a post stops notifying you (with Undo), or Decline a group invite or an ask to reply. Declining checks with you first, because it cannot be undone.
Clearing it
Mark all read, on the All tab, marks every unread notification read after you confirm. Read notifications stay in the list below any new ones.
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