My table looks like this:
id | user_id | period_id | completed_on
----------------------------------------
1 | 1 | 1 | 2010-01-01
2 | 2
Seems like this should work using MAX
and a subquery:
SELECT t.Id, t.User_Id, t.Period_Id, t.Completed_On
FROM my_table t
JOIN (SELECT Max(completed_on) Max_Completed_On, t.User_Id
FROM my_table
GROUP BY t.User_ID
) t2 ON
t.User_Id = t2.User_Id AND t.Completed_On = t2.Max_Completed_On
However, if you potentially have multiple records where the completed_on date is the same per user, then this could return multiple records. Depending on your needs, potentially adding a MAX(Id) in your subquery and joining on that would work.