The ability to induce desired shape and topographical changes in matter on demand is key to future advances in materials science and robotics. An important class of shape-morphing solids is characterized by spatially programmable anisotropic deformations that can be activated through a variety of stimuli, including light, heat, and pressure. We use the word nematic to describe such solids, borrowing a term from liquid crystal theory. We highlight the diversity of nematics that have been developed in recent years and review their distinguishing geometric and mechanical features, with a focus on thin shape-morphing sheets. We showcase how shape-morphing nematic systems can be designed to execute mechanical tasks. We end with an exploration of the challenges and opportunities involving the control of shape-morphing systems, which will be necessary for more advanced applications in robotics and is thus a key frontier in the field.