In recent years, jointless soft robots have demonstrated various curvilinear motions unlike conventional robotic systems requiring complex mechanical joints and electrical design principles. The materials employed to construct soft robots are mainly programmable anisotropic polymeric materials to achieve contactless manipulation of miniaturized and lightweight soft robots through their anisotropic strain responsivity to external stimuli. Although reviews on soft actuators are extensive, those on untethered soft robots are scant. In this study, we focus on the recent progress in the manipulation of untethered soft robots upon receiving external stimuli such as magnetic fields, light, humidity, and organic solvents. For each external stimulus, we provide an overview of the working principles along with the characteristics of programmable anisotropic materials and polymeric composites used in soft robotic systems. In addition, potential applications for untethered soft robots are discussed based on the physicochemical properties of programmable anisotropic materials for the given external stimuli.