The human eye is a remarkable imaging device, with many attractive design features. Prominent among these is a hemispherical detector geometry, similar to that found in many other biological systems, that enables a wide field of view and low aberrations with simple, few-component imaging optics. This type of configuration is extremely difficult to achieve using established optoelectronics technologies, owing to the intrinsically planar nature of the patterning, deposition, etching, materials growth and doping methods that exist for fabricating such systems. Here we report strategies that avoid these limitations, and implement them to yield high-performance, hemispherical electronic eye cameras based on single-crystalline silicon. The approach uses wafer-scale optoelectronics formed in unusual, two-dimensionally compressible configurations and elastomeric transfer elements capable of transforming the planar layouts in which the systems are initially fabricated into hemispherical geometries for their final implementation. In a general sense, these methods, taken together with our theoretical analyses of their associated mechanics, provide practical routes for integrating well-developed planar device technologies onto the surfaces of complex curvilinear objects, suitable for diverse applications that cannot be addressed by conventional means.