Leveraging massive numbers of sensors in user equipment as well as opportunistic human mobility, mobile crowd sensing (MCS) has emerged as a powerful paradigm, where prolonging battery life of constrained devices and motivating human involvement are two key design challenges. To address these, we envision a novel framework, named wirelessly powered crowd sensing (WPCS), which integrates MCS with wireless power transfer (WPT) for supplying the involved devices with extra energy and thus facilitating user incentivization. This paper considers a multiuser WPCS system where an access point (AP) transfers energy to multiple mobile sensors (MSs), each of which performs data sensing, compression, and transmission. Assuming lossless (data) compression, an optimization problem is formulated to simultaneously maximize data utility and minimize energy consumption at the operator side, by jointly controlling wireless-power allocation at the AP as well as sensing-data sizes, compression ratios, and sensor-transmission durations at the MSs. Given fixed compression ratios, the proposed optimal power allocation policy has the threshold-based structure with respect to a defined crowd-sensing priority function for each MS depending on both the operator configuration and the MS information. Further, for fixed sensing-data sizes, the optimal compression policy suggests that compression can reduce the total energy consumption at each MS only if the sensing-data size is sufficiently large. Our solution is also extended to the case of lossy compression, while extensive simulations are offered to confirm the efficiency of the contributed mechanisms.