The FCC used to give all exams. As the volume grew, conducting exams was delegated to a number of Volunteer Exam Coordinators (VECs) including the ARRL and their Volunteer Examiners. Our club's team is exploring the use of an online system to help us be more productive and serve people better.
Volunteer Examiner Coordinators
There is more than one! The official list of VECs show a number of groups organized like the ARRL that help the FCC proctor and submit exam results in the US. Questions for all VECs come from question pools of the www.ncvec.org. These Technician, General and Amateur Extra pools are updated in alternating years in July.
Exam.Tools aka examtools.org and its sister site HamStudy.org have been used by people to practice exam questions and pass exams. The system is sponsored by SignalStuff.com. A number of VECs use it to administer online and in-person exams.