Both the draft and registration were abolished January 27, 1973. In 1980, Jimmy Carter reinstated registration, however, Congressional Approval is required to reinstate the draft. Carter's rationalization was that we needed the ability to call up all registrants for national emergencies, not merely military duty. The registration process is not the same as it was before it was canceled. It is now inclusive of all male inhabitants of the United States, including undocumented aliens. Failure to register within 30 days of an 18th birthday is subject to 5 years in prison and a $250k fine. It is not called a Military Registration and Conscription System, but a Selective Service Registration. The prior system allowed for registration at 17, within 6 months of the 18th birthday, the age at which a man could enlist without parental approval. Males in prison or facilities for housing the insane, mental or physical incapacitation were exempt from registration (not to be confused with exemptions from the draft). There no local draft boards, only single central headquarters. No allowances for draft center physicals. No categorizations based on physical anomalies and no exemptions based on occupation or continuing education, or being a parent. So understand if you are blind police officer with 6 kids attending college at night, you are getting called up if and when the time comes.
"Still" is the wrong word because of the disruption and changes. I'm not sure what the right word might be. Don't argue with me about it, take it up with Jimmy Carter.