The wavefront sensor (WFS) is perhaps the most critical adaptive-optic subsystem, particularly for astronomical applications with natural guide stars, where current WFS sensitivity limitations seriously restrict sky coverage. In this paper, we discuss the possibility of a WFS based on a phase-contrast principle of the sort employed by Zernike for microscopy. Such a WFS would be implemented by inserting a focal-plane filter with a (pi) /2 phase-shifting central spot having a transverse size of the order of the diffraction limit. The result would be an image of the pupil in which intensity is directly proportional to the seeing- and aberration-induced phase variations over the pupil. In comparison, the signals produced by the two most common current WFS schemes, Shack-Hartmann and curvature sensing, are proportional to the phase slope and to the second derivative, respectively. The phase-contrast approach might derive some advantages stemming from its more natural match to the control eigenvectors of the electrostrictive deformable mirrors that are expected to predominate in high-order adaptive optics systems, in the same way that curvature sensors are currently well matched to bimorph mirrors. It may thus yield substantial performance improvements with simpler hardware and lighter computational loads. We examine this and other possible advantages of the phase-contrast WFS, and investigate some of the practical design issues involved in its implementation.