Shape-morphing structures are physical systems that can transition (morph) from one geometric state to another. They find applications in diverse fields, for example as deployable solar panels for satellites, medical implants such as heart stents, morphable air foils, smart textiles, soft robotics, building instrumentation, or tissue engineering. The shape-morphing deformation can be initiated by external forces, for example, a sheet of paper folded into an elaborate origami shape, or triggered by an internal actuation mechanism, such as inflation or swelling. Tremendous progress has been made in recent years in material science, mechanical engineering, and digital fabrication technologies. However, there are currently only very limited solutions to aid the design of shape-morphing surfaces. The intricate coupling of geometry, material, and actuation leads to highly complex shape spaces that cannot be explored effectively with existing tools. New computational methods are thus required to realize the full potential of shape-morphing surfaces and move beyond the limited set of geometries possible today. In this project we focus on deployable surfaces that can be fabricated in a planar state and then be actuated to a programmed 3D target state. This means that the deployed state is encoded in the 2D material through locally prescribed deformation behavior. Our central goal is to develop novel computational tools for inverse design of such shape-morphing surfaces, that is, to find a suitable flat 2D material state that can be automatically deployed to a functional 3D target shape.