The Managed Migrations team will send you a weekly migration status report, which looks like the one below. This article explains some of the key parts of that report.
Mailbox Shuttle Mapping Statistics
– Showing general mapping statistics till the day the report was created, overall completed migrations and failed migrations till the day of report creation
Issues & Next steps
– The last section contains some information about issues encountered during the last week and next steps how to resolve the issue, or what actions need to be done