Deep convolutional neural networks (CNNs) achieve state-of-the-art accuracy for many computer vision tasks. But using them for video monitoring applications incurs high computational cost and inference latency. Thus, recent works have studied how to improve system efficiency. But they largely focus on small closed world prediction vocabularies even though many applications in surveillance security, traffic analytics, etc. have an ever-growing set of target entities. We call this the unbounded vocabulary issue, and it is a key bottleneck for emerging video monitoring applications. We present the first data system for tacking this issue for video querying, Panorama. Our design philosophy is to build a unified and domain-agnostic system that lets application users generalize to unbounded vocabularies in an out-of-the-box manner without tedious manual re-training. To this end, we synthesize and innovate upon an array of techniques from the ML, vision, databases, and multimedia systems literature to devise a new system architecture. We also present techniques to ensure Panorama has high inference efficiency. Experiments with multiple real-world datasets show that Panorama can achieve between 2x to 20x higher efficiency than baseline approaches on in-vocabulary queries, while still yielding comparable accuracy and also generalizing well to unbounded vocabularies.