The insect compound eye is the most abundant eye architecture on earth. It comes in a wide variety of shapes and sizes, which are exquisitely adapted to specific ecosystems. Here, we explore the organisational principles and pathways, from molecular to tissular, that underpin the building of this organ and highlight why it is an excellent model system to investigate the relationship between genes and tissue form. The compound eye offers wide fields of view, high sensitivity in motion detection and infinite depth of field. It is made of an array of visual units called ommatidia, which are precisely tiled in 3D to shape the retinal tissue as a dome-like structure. The eye starts off as a 2D epithelium, and it acquires its 3D organisation as ommatidia get into shape. Each ommatidium is made of a complement of retinal cells, including light-detecting photoreceptors and lens-secreting cells. The lens cells generate the typical hexagonal facet lens that lies atop the photoreceptors so that the eye surface consists of a quasi-crystalline array of these hexagonal facet-lenses. This array is curved to various degree, depending on the size and shape of the eye, and on the region of the retina. This curvature sets the resolution and visual field of the eye and is determined by i) the number and size of the facet lens – large ommatidial lenses can be used to generate flat, higher resolution areas, while smaller facets allow for stronger curvature of the eye, and ii) precise control of the inter facet-lens angle, which determines the optical axis of the each ommatidium. In this review we discuss how combinatorial variation in eye primordium shape, ommatidial number, facet lens size and inter facet-lens angle underpins the wide variety of insect eye shapes, and we explore what is known about the mechanisms that might control these parameters.