Images of the eye are key in several computer vision problems, such as shape registration and gaze estimation. Recent large-scale supervised methods for these problems require time-consuming data collection and manual annotation, which can be unreliable. We propose synthesizing perfectly labelled photo-realistic training data in a fraction of the time. We used computer graphics techniques to build a collection of dynamic eye-region models from head scan geometry. These were randomly posed to synthesize close-up eye images for a wide range of head poses, gaze directions, and illumination conditions. Finally, we demonstrate the benefits of our synthesized training data (SynthesEyes) by out-performing state-of-the-art methods for eye-shape registration as well as cross-dataset appearance-based gaze estimation in the wild.