What the history tracks, who each line is recorded against, and what it deliberately does not record.
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The history is an account of what happened to the ticket, not a chat. It records status changes with the status it moved from and to, assignment changes, and the significant events on the other tabs of the ticket.
Each entry is recorded against whoever was signed in when it happened. It cannot be recorded under somebody else. That includes repeating tickets: the person who presses Complete is the person the history and the alerts name, whoever else is involved in the work.
Ordinary edits to a description are not tracked, and neither is anything that failed. This matters when you are reading a history to work out what happened: a missing line means the action did not happen, not that it happened quietly.
Archiving a ticket does not clear its history.