The horopter's history may partly be responsible for its ambiguous psychophysical definitions and obscured physiological significance. However, the horopter is a useful clinical tool integrating physiological optics and binocular vision. This article aims to help understand how it could come to such different attitudes toward the horopter. After the basic concepts underlying binocular space perception and stereopsis are presented, the horopter's old ideas that influence today's research show their inconsistencies with the conceptualized binocular vision. Two recent geometric theories of the horopter with progressively higher eye model fidelity that resolve the inconsistencies are reviewed. The first theory corrects the 200-year-old Vieth-Müller circle still used as a geometric horopter. The second theory advances Ogle's classical work by modeling empirical horopters as conic sections in the binocular system with the asymmetric eye model that accounts for the observed misalignment of optical components in human eyes. Its extension to iso-disparity conics is discussed.
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