Coactive Design is a new approach to address the increasingly sophisticated roles that people and robots play as the use of robots expands into new, complex domains. The approach is motivated by the desire for robots to perform less like teleoperated tools or independent automatons and more like interdependent teammates. In this article, we describe what it means to be interdependent, why this is important, and the design implications that follow from this perspective. We argue for a human-robot system model that supports interdependence through careful attention to requirements for observability, predictability, and directability. We present a Coactive Design method and show how it can be a useful approach for developers trying to understand how to translate high-level teamwork concepts into reusable control algorithms, interface elements, and behaviors that enable robots to fulfill their envisioned role as teammates. As an example of the coactive design approach, we present our results from the DARPA Virtual Robotics Challenge, a competition designed to spur development of advanced robots that can assist humans in recovering from natural and man-made disasters. Twenty-six teams from eight countries competed in three different tasks providing an excellent evaluation of the relative effectiveness of different approaches to human-machine system design.