The Notification panel, available from the top right of the screen should provide details about Translation activities.
Ideally, the user that has triggered the job should at least be notified of its status.
Definitely a familiar request, thanks! See comments on what else we'd want before adding this type of notification.
Update: Though this is great idea, this specific request is currently not planned based on our program planning and prioritization of all Tridion Sites ideas for early 2018. We may revisit this and other great ideas based on more information and additional votes.
Status of translation is possible through Translation Review, as part of workflow, or through a Notification API extension.
The Notification panel, available from the top right of the screen should provide details about Translation activities.
Ideally, the user that has triggered the job should at least be notified of its status.