Sleep monitoring is essential to people's health and wellbeing, which can also assist in the diagnosis and treatment of sleep disorder. Compared with contact-based solutions, contactless sleep monitoring does not attach any device to the human body; hence, it has attracted increasing attention in recent years. Inspired by the recent advances in Wi-Fi-based sensing, this article proposes a low-cost and nonintrusive sleep monitoring system using commodity Wi-Fi devices, namely, WiFi-Sleep. We leverage the fine-grained channel state information from multiple antennas and propose advanced fusion and signal processing methods to extract accurate respiration and body movement information. We introduce a deep learning method combined with clinical sleep medicine prior knowledge to achieve four-stage sleep monitoring with limited data sources (i.e., only respiration and body movement information). We benchmark the performance of WiFi-Sleep with polysomnography, the gold reference standard. Results show that WiFi-Sleep achieves an accuracy of 81.8%, which is comparable to the state-of-the-art sleep stage monitoring using expensive radar devices.