To View Backup History of All Databases

--for specific database
USE msdb;
GO

SELECT b.database_name,
 bm.physical_device_name,
 b.backup_start_date,
 b.backup_finish_date
FROM dbo.backupset b
JOIN dbo.backupmediafamily bm
 ON b.media_set_id = bm.media_set_id
WHERE b.database_name = 'YourDatabaseName'
ORDER BY b.backup_finish_date DESC;

--for all databases
SELECT bs.database_name,
 bs.backup_start_date,
 bs.backup_finish_date,
 bs.server_name,
 bs.user_name,
 bs.type,
 bm.physical_device_name
FROM msdb.dbo.backupset AS bs
INNER JOIN msdb.dbo.backupmediafamily AS bm on bs.media_set_id = bm.media_set_id

--or

SELECT database_name,
 backup_size/1024/1024 AS 'Backup Size in MB',
 backup_start_date,
 backup_finish_date,
 CASE type
 WHEN 'D' THEN 'Full'
 WHEN 'I' THEN 'Differential'
 WHEN 'L' THEN 'Transaction Log'
 END AS 'Backup Type'
FROM msdb.dbo.backupset
WHERE backup_start_date > DATEADD(mm, -1, GETDATE())
ORDER BY backup_start_date DESC;