Optical models of the human eye have been used in visual science for purposes such as providing a framework for explaining optical phenomena in vision, for predicting how refraction and aberrations are affected by change in ocular biometry and as computational tools for exploring the limitations imposed on vision by the optical system of the eye. We address the issue of what is understood by optical model eyes, discussing the 'encyclopaedia' and 'toy train' approaches to modelling. An extensive list of purposes of models is provided. We discuss many of the theoretical types of optical models (also schematic eyes) of varying anatomical accuracy, including single, three and four refracting surface variants. We cover the models with lens structure in the form of nested shells and gradient index. Many optical eye models give accurate predictions only for small angles and small fields of view. If aberrations and image quality are important to consider, such 'paraxial' model eyes must be replaced by 'finite model' eyes incorporating features such as aspheric surfaces, tilts and decentrations, wavelength-dependent media and curved retinas. Many optical model eyes are population averages and must become adaptable to account for age, gender, ethnicity, refractive error and accommodation. They can also be customised for the individual when extensive ocular biometry and optical performance data are available. We consider which optical model should be used for a particular purpose, adhering to the principle that the best model is the simplest fit for the task. We provide a glimpse into the future of optical models of the human eye. This review is interwoven with historical developments, highlighting the important people who have contributed so richly to our understanding of visual optics.Key words: finite models, optical models, paraxial models, schematic eyes, visual optics During their investigations in vision science, both authors have relied heavily on optical models of the eye. Their reasons for developing and using these include establishing a framework for explaining optical phenomena in vision, for predicting how aberrations are affected by change in ocular biometry and as a computational tool for exploring the limitations imposed on vision by the optical system of the eye. It seems fitting to assemble our ideas on the subject here, as well as to acknowledge our forebears and colleagues. To develop the flow of ideas, we have omitted equations.We begin by asking 'What is an optical model eye, anyway?' A short answer is that optical models summarise and organise our understanding of the eye as an optical system and provide a conceptual framework for thinking about how the retinal image is formed to launch the visual process. Eye models fall into two different categories. One is the 'encyclopaedia' type of model, which means that the model is a mechanistic summary of everything we know about the eye's optical system and how it works. The encyclopaedic model is a compact, working representation of knowledge about ocular...