For decades, the design of untethered devices has been focused on delivering a fixed quality of service with minimum power consumption, to enable battery-powered devices with reasonably long deployment lifetime. However, to realize the promised tens of billions of connected devices in the Internet of Things, computers must operate autonomously and harvest ambient energy to avoid the cost and maintenance requirements imposed by mains- or battery-powered operation. But harvested power typically fluctuates, often unpredictably, and with large temporal and spatial variability. Energy-driven computers are designed to treat energy-availability as a first-class citizen, in order to gracefully adapt to the dynamics of energy harvesting. They may sleep through periods of no energy, endure periods of scarce energy, and capitalize on periods of ample energy. In this paper, we describe the promise and limitations of energy-driven computing, with an emphasis on intermittent operation. This article is part of the theme issue 'Harmonizing energy-autonomous computing and intelligence'.