Recent research has demonstrated that emotion plays a key role in human decision making. Across a wide range of disciplines, old concepts, such as the classical ``rational actor" model, have fallen out of favor in place of more nuanced models (e.g., the frameworks of behavioral economics and emotional intelligence) that acknowledge the role of emotions in analyzing human actions. We now know that context, framing, and emotional and physiological state can all drastically influence decision making in humans. Emotions serve an essential, though often overlooked, role in our lives, thoughts, and decisions. However, it is not clear how and to what extent emotions should impact the design of artificial agents, such as social robots. In this paper I argue that enabling robots, especially those intended to interact with humans, to sense and model emotions will improve their performance across a wide variety of human-interaction applications. I outline two broad research topics (affective inference and learning from affect) towards which progress can be made to enable ``affect-aware" robots and give a few examples of applications in which robots with these capabilities may outperform their non-affective counterparts. By identifying these important problems, both necessary for fully affect-aware social robots, I hope to clarify terminology, assess the current research landscape, and provide goalposts for future research.