This paper reviews advances in our knowledge about the stability of the human being's line of sight while fixating objects stationary with respect to himself. Recent technological developments made it possible to measure gaze with a high degree of accuracy when the head was free of artificial support. Measurements made with the head free while the subject sat, as still as possible, show that gaze is half as stable as when the head is held rigidly. Precision deteriorates by an additional factor of five when the head is moved actively or passively within a range of natural physiological frequencies and amplitudes. Fixation errors and retinal image motions associated with such imprecision of gaze under natural conditions would not be expected to degrade monocular vision in light of current psychophysical evidence. Binocular fixation errors and differences in retinal image motions in each of the eyes, associated with imprecision of vergence under natural conditions, cannot, however, be reconciled with current psychophysical knowledge of binocular vision attained thus far only under artificial conditions.