Monitoring refers to checking database status, settings which can be the owner’s name, file names, file sizes, backup schedules, etc.
SQL Server databases can be monitored mainly through SQL Server Management Studio or T-SQL, and also can be monitored through various methods like creating agent jobs and configuring database mail, third party tools, etc.
Database status can be checked whether it is online or in any other state as shown in the following snapshot.
As per the above screen, all databases are in 'Online' status. If any database is in any other state, then that state will be shown as shown in the following snapshot.