The vast adoption of mobile devices with cameras has greatly contributed to the proliferation of the creation and distribution of videos. For a variety of purposes, valuable information may be extracted from these videos. While the computational capability of mobile devices has greatly improved recently, video processing is still a demanding task for mobile devices. We design an on-demand video processing system, NetVision, that performs distributed video processing using deep learning across a wireless network of mobile devices and video-clouds to answer queries while minimizing the query response time. However, the problem of minimal query response time for processing videos stored across a network is a strongly NP-hard problem. To deal with this, we design a greedy algorithm with bounded performance. To further deal with the dynamics of the transmission rate between mobile devices and video-clouds, we design an adaptive algorithm. We built NetVision and deployed it on a small testbed. Based on the measurements of the testbed and by extensive simulations, we show that the greedy algorithm is close to the optimum and the adaptive algorithm performs better with more dynamic transmission rates. We then perform experiments on the small testbed to examine the realized system performance in both stationary networks and mobile networks.