Over the past decade, soft robot research has expanded to diverse fields, including biomedicine, bionics, service robots, human–robot interaction, and artificial intelligence. Much work has been done in modeling the kinematics and dynamics of soft robots, but closed‐loop control is still in its early stages due to limited sensory feedback. Thanks to the advancement in functional materials, structures, and manufacturing techniques for flexible electronics, flexible and stretchable sensors are developing rapidly. These sensors provide feedback for closed‐loop control tasks and enable soft robots to effectively explore the unknown and safely interact with humans and the environment. Herein, recent advances in perceptive soft robots that utilize flexible/stretchable sensors and functional materials are outlined. The perceptive functions of soft robots from two different aspects, that is, proprioception and exteroception, are summarized. Furthermore, the constructions of autonomous soft robots by integrating both proprioceptive and exteroceptive capabilities for closed‐loop control tasks and other challenging tasks in the real world are discussed.