MarkerInbound and alexb757 are mostly correct, save for a minor error about the requirement of Medical Certificates for Airline Transport Pilot certificate applicants.
You are not required to hold any medical certificate to take the "Knowledge" (written) Exam for an ATP and only require a Third Class medical certificate when taking a practical test in an aircraft for the airline transport pilot certificate.
In the event that the practical test is a simulator, then no valid medical certificate is required. However, you require a valid first-class medical certificate when exercising the privileges of an airline transport pilot certificate (14 CFR 61.23).