Time Machine external drive filling up

The external drive I use for Time Machine on my iMac is starting to fill up. The backups go back a very long way (ie almost three years). Does Time Machine automatically delete the earliest backups as the external drive fills up or do I have to delete these manually? If manually, is there any harm in my deleting all the back-ups up until say a month ago, or should I keep the very earliest backups on the basis that these will contain eg system information that might be useful if I have a major crash?