• Log shipping is a disaster recovery solution from Microsoft. Log Shipping comes up with multiple internal tables to refer to its details and monitor current status.
• log_shipping_monitor_alert – This SYSTEM table saves alert CONFIGURATION used to monitor and trigger a notification on violations.
• log_shipping_monitor_error_detail – This system table shows errors occurred during Log shipping.
• log_shipping_monitor_history_detail – This system table saves the history of log shipping and it’s status. This can be referred in future for any issues and security report.
• log_shipping_monitor_primary – These tables save one record per database with backup and MONITORING threshold.
• log_shipping_monitor_secondary - These tables save one record per secondary database with the primary server, primary database, restore and monitoring threshold.
• log_shipping_primary_databases – This table saves a list of all databases serving as primary database & enabled for Log shipping.
• Log_shipping_secondary_databases - This table saves a list of all databases serving as a secondary database in Log shipping.

Also, You can use the Transaction Log Shipping Report at Server Level to VIEW the current status.