Compatibility level of SQL Server
To know  the current compatibility_level of your database you can run:

SELECT name,compatibility_level 
FROM sys.databases 
WHERE name = 'DatabaseName';


Result for my TEST database:

name    compatibility_level
TEST    140


If the compatibility level changes, for example with the command:

ALTER DATABASE TEST SET COMPATIBILITY_LEVEL = 120;


You could find the date and time that happened in the sql server error log:




Or reading the (current) error log file with xp_readerrorlog: 

EXEC sp_readerrorlog 0, 1, 'COMPATIBILITY_LEVEL' 


Result



Replace the first parameter of xp_readerrorlog to 1 to read the second error log file, 2 for the third file, ... .