Laser spectroscopy of atomic hydrogen has been important in the recent development of Doppler-free laser techniques and offers stringent tests of atomic theory together with precise measurements of fundamental atomic constants. In this review we outline the theory of the structure of atomic hydrogen and describe the techniques of Doppler-free laser spectroscopy. This field has been extremely active in recent years and we bring together the most recent results of measurements of the Rydberg constant and the ground-state Lamb shift.