Videos take a lot of time to transport over the network, hence running analytics on the live video on embedded or mobile devices has become an important system driver. Considering such devices, e.g., surveillance cameras or AR/VR gadgets, are resource constrained, although there has been significant work in creating lightweight deep neural networks (DNNs) for such clients, none of these can adapt to changing runtime conditions, e.g., changes in resource availability on the device, the content characteristics, or requirements from the user. In this article, we introduce ApproxNet, a video object classification system for embedded or mobile clients. It enables novel dynamic approximation techniques to achieve desired inference latency and accuracy trade-off under changing runtime conditions. It achieves this by enabling two approximation knobs within a single DNN model rather than creating and maintaining an ensemble of models, e.g., MCDNN [MobiSys-16]. We show that ApproxNet can adapt seamlessly at runtime to these changes, provides low and stable latency for the image and video frame classification problems, and shows the improvement in accuracy and latency over ResNet [CVPR-16], MCDNN [MobiSys-16], MobileNets [Google-17], NestDNN [MobiCom-18], and MSDNet [ICLR-18].