Internet-of-Things (IoT) devices are becoming both intelligent and green. On the one hand, Deep Neural Network (DNN) compression techniques make it possible to run deep learning applications on devices equipped with low-end microcontrollers (MCUs). By performing deep learning on IoT devices, in-situ decision-making can be made, which can improve the responsiveness of such devices to the environment and reduce data uploading to edge servers or clouds to save valuable network bandwidth. On the other hand, many IoT devices in the future will be powered by energy harvesters instead of batteries to reduce environmental pollution and achieve permanent service free of battery maintenance. As the energy output of energy harvesters is tiny and unstable, energy harvesting IoT (EH-IoT) devices will experience frequent power failures during their execution, making the software task hard to progress. The deep learning tasks running on such devices must face this challenge and, at the same time, ensure satisfactory execution efficiency. We believe deploying deep learning on EH-IoT devices that execute intermittently will be a challenging yet promising research direction. To motivate research in this direction, this paper summarizes existing solutions and provides an in-depth discussion of future challenges that deserve further investigation. With IoT devices becoming more intelligent and green, DNN inference on EH-IoT devices will generate a much more significant impact in the future in academia and industry.