Getting the right amount of quality sleep is a key aspect of good health, along with a healthy diet and regular exercise. Human-computer interaction (HCI) researchers have recently designed systems to support diet and exercise, but sleep has been relatively under-studied in the HCI community. We conducted a literature review and formative study aimed at uncovering opportunities for computing to support the important area of promoting healthy sleep. We present results from interviews with sleep experts, as well as a survey (N = 230) and interviews with potential users (N = 16) to indicate what people would find practical and useful for sleep. Based on these results, we identify a number of design considerations, challenges, and opportunities for using computing to support healthy sleep behaviors, as well as a design framework for mapping the design space of technologies for sleep.