This paper presents a general theory for the remote estimation of the point-of-gaze (POG) from the coordinates of the centers of the pupil and corneal reflections. Corneal reflections are produced by light sources that illuminate the eye and the centers of the pupil and corneal reflections are estimated in video images from one or more cameras. The general theory covers the full range of possible system configurations. Using one camera and one light source, the POG can be estimated only if the head is completely stationary. Using one camera and multiple light sources, the POG can be estimated with free head movements, following the completion of a multiple-point calibration procedure. When multiple cameras and multiple light sources are used, the POG can be estimated following a simple one-point calibration procedure. Experimental and simulation results suggest that the main sources of gaze estimation errors are the discrepancy between the shape of real corneas and the spherical corneal shape assumed