In this work we present RAPID, the first joint communication and radar system based on next-generation IEEE 802.11ay WiFi networks operating in the 60 GHz band. Unlike existing approaches for human sensing at millimeter-wave frequencies, which rely on special-purpose radars, RAPID achieves radar-level sensing accuracy with IEEE 802.11ay access points, thus avoiding the burden of installing ad-hoc sensors. RAPID enables contactless human sensing applications, such as people tracking, Human Activity Recognition (HAR), and person identification without requiring modifications to the standard packet structure. Specifically, we leverage IEEE 802.11ay beam training to accurately localize and track multiple individuals within the same environment. Then, we propose a new way of using beam tracking to extract micro-Doppler signatures from the time-varying Channel Impulse Response (CIR) estimated fromreflectedpackets. Such signatures are fed to a deep learning classifier to perform HAR and person identification. RAPID is implemented on a cutting-edge IEEE 802.11ay-compatible FPGA platform with phased antenna arrays, and evaluated on a large dataset of CIR measurements. It is robust across different environments and subjects, and outperforms state-of-the-art sub-6 GHz WiFi sensing techniques. Using two access points, RAPID reliably tracks multiple subjects, reaching HAR and person identification accuracies of$94\%$and$90\%$, respectively.