Morphology plays an important role in behavioral and locomotion strategies of living and artificial systems. There is biological evidence that adaptive morphological changes can not only extend dynamic performances by reducing tradeoffs during locomotion but also provide new functionalities. In this article, we show that adaptive morphology is an emerging design principle in robotics that benefits from a new generation of soft, variable-stiffness, and functional materials and structures. When moving within a given environment or when transitioning between different substrates, adaptive morphology allows accommodation of opposing dynamic requirements (e.g., maneuverability, stability, efficiency, and speed). Adaptive morphology is also a viable solution to endow robots with additional functionalities, such as transportability, protection, and variable gearing. We identify important research and technological questions, such as variable-stiffness structures, in silico design tools, and adaptive control systems to fully leverage adaptive morphology in robotic systems.