For flights within the US in the very near future, no medical will be required. Flights outside the US will still require a medical.
Under the BasicMed reform, student pilots will have to pass a FAA medical to get into the system unless they're just getting a glider or balloon rating or a sport pilot certificate. After that no medical will be required until the pilot moves up to commercial operations or flys an airplane with more than 6 seats or weights more than 6,000 pounds. Or they want to fly faster than 250 knots or above FL180. Then they'll need a FAA medical.