Most in-the-wild images are stored in Low Dynamic Range (LDR) form, serving as a partial observation of the High Dynamic Range (HDR) visual world.Despite limited dynamic range, these LDR images are often captured with different exposures, implicitly containing information about the underlying HDR image distribution.Inspired by this intuition, in this work we present, to the best of our knowledge, the first method for learning a generative model of HDR images from in-the-wild LDR image collections in a fully unsupervised manner. The key idea is to train a generative adversarial network (GAN) to generate HDR images which, when projected to LDR under various exposures, are indistinguishable from real LDR images.The projection from HDR to LDR is achieved via a camera model that captures the stochasticity in exposure and camera response function.Experiments show that our method GlowGAN can synthesize photorealistic HDR images in many challenging cases such as landscapes, lightning, or windows, where previous supervised generative models produce overexposed images. With the assistance of GlowGAN, we showcase the novel application of unsupervised inverse tone mapping (GlowGAN-ITM) that sets a new paradigm in this field. Unlike previous methods that gradually complete information from LDR input, GlowGAN-ITM searches the entire HDR image manifold modeled by GlowGAN for the HDR images which can be mapped back to the LDR input. GlowGAN-ITM achieves more realistic reconstruction of overexposed regions compared to state-of-the-art supervised learning models, despite not requiring HDR images or paired multi-exposure images for training.