Authoring high-quality digital materials is key to realism in 3D rendering. We circumvent this limitation by proposing PhotoMat: the first material generator trained exclusively on real photos of material samples captured using a cell phone camera with flash. Supervision on individual material maps is not available in this setting. Instead, we train a generator for a neural material representation that is rendered with a learned relighting module to create arbitrarily lit RGB images; these are compared against real photos using a discriminator. We train PhotoMat with a new dataset of 12,000 material photos captured with handheld phone cameras under flash lighting. We demonstrate that our generated materials have better visual quality than previous material generators trained on synthetic data. Moreover, we can fit analytical material models to closely match these generated neural materials, thus allowing for further editing and use in 3D rendering.