Facial caricature is an art form of drawing faces in an exaggerated way to convey humor or sarcasm. In this paper, we propose the first Generative Adversarial Network (GAN) for unpaired photo-to-caricature translation, which we call "CariGANs". It explicitly models geometric exaggeration and appearance stylization using two components: CariGeoGAN, which only models the geometry-to-geometry transformation from face photos to caricatures, and CariStyGAN, which transfers the style appearance from caricatures to face photos without any geometry deformation. In this way, a difficult cross-domain translation problem is decoupled into two easier tasks. The perceptual study shows that caricatures generated by our CariGANs are closer to the hand-drawn ones, and at the same time better persevere the identity, compared to state-of-the-art methods. Moreover, our CariGANs allow users to control the shape exaggeration degree and change the color/texture style by tuning the parameters or giving an example caricature.