You can choose to receive an email notification every time your report runs. Find out how here.
It's also possible to check the status of each report on the Location Dashboard. If it says ‘Updating data...’ under the tool’s name in the sidebar, this means the report is still running. The report is ready to be viewed if you don't see this message.
In the above example, the Rank Tracker report is still running, but the Citation Tracker, Reputation Manager, Google Business Profile Audit and Local Search Audit reports are ready to view.