Crystal-structure phase mapping is a core, long-standing challenge in materials science that requires identifying crystal phases, or mixtures thereof, in X-ray diffraction measurements of synthesized materials. Phase mapping algorithms have been developed that excel at solving systems with up to several unique phase mixtures, where each phase has a readily distinguishable diffraction pattern. However, phase mapping is often beyond materials scientists’ capabilities and also poses challenges to state-of-the-art algorithms due to complexities such as the existence of dozens of phase mixtures, alloy-dependent variation in the diffraction patterns and multiple compositional degrees of freedom, creating a major bottleneck in high-throughput materials discovery. Here we show how to automate crystal-structure phase mapping. We formulate phase mapping as an unsupervised pattern demixing problem and describe how to solve it using deep reasoning networks (DRNets). DRNets combine deep learning with constraint reasoning for incorporating prior scientific knowledge and consequently require only a modest amount of (unlabelled) data. DRNets compensate for the limited data by exploiting and magnifying the rich prior knowledge about the thermodynamic rules governing the mixtures of crystals. DRNets are designed with an interpretable latent space for encoding prior-knowledge domain constraints and seamlessly integrate constraint reasoning into neural network optimization. DRNets surpass previous approaches on crystal-structure phase mapping, unravelling the Bi–Cu–V oxide phase diagram and aiding the discovery of solar fuels materials.