As robots move beyond manufacturing applications to less predictable environments, they increasingly can benefit, as animals do, from integrating sensing and control with the passive properties provided by particular combinations and arrangements of materials and mechanisms. This realization is partly responsible for the recent proliferation of soft and bioinspired robots. However, many structures and mechanisms in nature are not uniformly soft. Rather, they are selectively soft – highly compliant in certain directions, or when loaded in a certain way, but stiff or inextensible when loaded differently. Such tuned materials and mechanisms, whether in animals or robots, can provide several kinds of benefits, including energy storage and recovery, increased physical robustness, and decreased response time to sudden events. This talk will explore these interrelated concepts using examples from several bioinspired mobile robots that exploit selectively soft materials and structures when interacting with objects and surfaces in the environment.