The formation of well-defined and functional three-dimensional (3D) structures by buckling of thin sheets subjected to spatially nonuniform stresses is common in biological morphogenesis and has become a subject of great interest in synthetic systems, as such programmable shape-morphing materials hold promise in areas including drug delivery, biomedical devices, soft robotics, and biomimetic systems. Given their ability to undergo large changes in swelling in response to a wide variety of stimuli, hydrogels have naturally emerged as a key type of material in this field. Of particular interest are hybrid systems containing rigid inclusions that can define both the anisotropy and spatial nonuniformity of swelling as well as nanoparticulate additives that can enhance the responsiveness and functionality of the material. In this Account, we discuss recent progress in approaches to achieve well-defined shape morphing in hydrogel hybrids. First, we provide an overview of materials and methods that facilitate fabrication of such systems and outline the geometry and mechanics behind shape morphing of thin sheets. We then discuss how patterning of stiff inclusions within soft responsive hydrogels can be used to program both bending and swelling, thereby providing access to a wide array of complex 3D forms. The use of discretely patterned stiff regions to provide an effective composite response offers distinct advantages in terms of scalability and ease of fabrication compared with approaches based on smooth gradients within a single layer of responsive material. We discuss a number of recent advances wherein control of the mechanical properties and geometric characteristics of patterned stiff elements enables the formation of 3D shapes, including origami-inspired structures, concatenated helical frameworks, and surfaces with nonzero Gaussian curvature. Next, we outline how the inclusion of functional elements such as nanoparticles can enable unique pathways to programmable and even reprogrammable shape-morphing materials. We focus to a large extent on photothermally reprogrammable systems that include one of a variety of additives that serve to efficiently absorb light and convert it into heat, thereby driving the response of a temperature-sensitive hydrogel. Such systems are advantageous in that patterns of light can be defined with very high spatial and temporal resolution in addition to offering the potential for wavelength-selective addressability of multiple different inclusions. We highlight recent advances in the preparation of light-responsive hybrid systems capable of undergoing reprogrammable bending and buckling into well-defined 3D shapes. In addition, we describe several examples where shape tuning of hybrid systems enables control over the motion of responsive hydrogel-based materials. Finally, we offer our perspective on open challenges and future areas of interest for the field.