Glaucoma continues to be a mysterious disease. High intraocular pressure (IOP), once the landmark of the disease, has been relegated to the humble role of risk factor, despite the fact that lowering IOP continues to be the only partially successful treatment. Even with an IOP successfully controlled to statistical standards, many patients still mysteriously continue to progressively lose neural tissue. A novel pathogenetical mechanism has recently been put forward as the main agent of the disease. In this new light, some structural details of the human eye, the result of the peculiar evolutionary development, take on an unexpected role in the presentation of the disease. As results of cladistics analysis, the human eye appears as particularly prone to suffering glaucoma as a consequence of the evolutionary path taken. That makes glaucoma essentially a human (and related hominid) scourge. Exclusive features of the human eye compared to other vertebrates involve both the anterior and posterior segment. Those features that facilitate glaucoma in humans are absent in many of the purported animal models for the disease, and this inadequacy further convolutes the mystery of glaucoma. This suggests the division of the animal models into those that mimic the whole disease and those that only reproduce a pertinent histological feature. Unfortunately most animal models are based on high intraocular pressure which excludes most cases of low or moderate pressure. For any animal model, it is important the researcher accurately establishes the constraints of the model in order to avoid jumping to conclusions.