This article explores the use of ambient radio frequency (RF) signals for human presence detection through deep learning. Using Wi-Fi signal as an example, we demonstrate that the channel state information (CSI) obtained at the receiver contains rich information about the propagation environment. Through judicious preprocessing of the estimated CSI followed by deep learning, reliable presence detection can be achieved. Several challenges in passive RF sensing are addressed. With presence detection, how to collect training data with human presence can have a significant impact on the performance. This is in contrast to activity detection when a specific motion pattern is of interest. A second challenge is that RF signals are complex-valued. Handling complex-valued input in deep learning requires careful data representation and network architecture design. Finally, human presence affects CSI variation along multiple dimensions; such variation, however, is often masked by system impediments, such as timing or frequency offset. Addressing these challenges, the proposed learning system uses preprocessing to preserve human motion-induced channel variation while insulating against other impairments. A convolutional neural network (CNN) properly trained with both magnitude and phase information is then designed to achieve reliable presence detection. Extensive experiments are conducted. Using off-the-shelf Wi-Fi devices, the proposed deep-learning-based RF sensing achieves near-perfect presence detection during multiple extended periods of test and exhibits superior performance compared with leading edge passive infrared sensors. A comparison with existing RF-based human presence detection also demonstrates its robustness in performance, especially when deployed in a completely new environment. The learning-based passive RF sensing thus provides a viable and promising alternative for presence or occupancy detection.