We propose, WarpGAN, a fully automatic network that can generate caricatures given an input face photo. Besides transferring rich texture styles, WarpGAN learns to automatically predict a set of control points that can warp the photo into a caricature, while preserving identity. We introduce an identity-preserving adversarial loss that aids the discriminator to distinguish between different subjects. Moreover, WarpGAN allows customization of the generated caricatures by controlling the exaggeration extent and the visual styles. Experimental results on a public domain dataset, WebCaricature, show that WarpGAN is capable of generating caricatures that not only preserve the identities but also outputs a diverse set of caricatures for each input photo. Five caricature experts suggest that caricatures generated by WarpGAN are visually similar to hand-drawn ones and only prominent facial features are exaggerated.