Difference between NOW(), SYSDATE() & CURRENT_DATE() in MySQL

CURRENT_DATE(): will only give you the date.
NOW(): give you the datetime when the statement,procedure etc… started.
SYSDATE(): give you the current datetime.
Look at the seconds after waiting 5 seconds between now()1 sysdate()1 with the following query (scroll to the right):

select now(),sysdate(),current_date(),sleep(5),now(),sysdate();

-- will give
-- now()                 sysdate()              current_date()          sleep(5)    now()1                sysdate()1
-- 6/10/2014 2:50:04 AM  6/10/2014 2:50:04 AM   6/10/2014 12:00:00 AM   0           6/10/2014 2:50:04 AM  6/10/2014 2:50:09 AM