Select mysql data starting from a specific date

I have player statistics which I would like to publish from certain dates. At the moment I can see statistics in the database from the begining.

SELECT name, 
       bankmoney AS Bank,
       Playerkills AS 'Player Kills',
       deathcount AS Deaths ,
       aikills AS 'AI Kills',
       teamkills AS 'Team Kills',
       revivecount AS Revives ,
       capturecount AS 'Territories Captured',
       LastModified AS 'Last Seen'
FROM playerinfo
JOIN playerstats
ON playerinfo.UID = playerstats.PlayerUID
ORDER BY BankMoney DESC;

But I would like to present statistics from the start of the day and the start of the week.

How would I do that ?